GIFT OF LPROF. W.B. RISING huribon HEAT BALFOUR STEWART EonDon MACMILLAN AND CO. PUBLISHERS TO THE UNIVERSITY OF iforfc Clarmtwtt AN ELEMENTARY TREATISE ON HEAT BY BALFOUR STEWART, LL.D. F.R.S. SUPERINTENDENT OF THE KEW OBSERVATORY EXAMINER AT THE UNIVERSITIES OF EDINBURGH AND LONDON xforfc AT THE CLARENDON PRESS M.DCCC.LXVI. PREFACE. IN this work the Author has endeavoured to place before his readers in an elementary form the facts and principles of the Science of 'Heat/ and also to give some of the most prominent practical applications of our knowledge of this subject. His object has been to begin with the study of well- ascertained facts and to proceed onwards to general principles. Accordingly, the work has been divided into three parts; the first of which embraces the study of the various effects produced by heat upon bodies. In this part many of the most recent investigations, as well as the apparatus used in conducting them, are described at length, while numerical examples are given, which, it is hoped, may enable the student to attain to the accuracy needful in physical research. The second division contains the laws which regulate the distribution of heat through space, and includes radiation, conduction, convection, and the measurements of specific and latent heat. Theoretical views are here for the first time introduced. The third and last part relates to the nature of Heat, its sources, and connection with other properties of matter. In this part Heat is viewed as a species of b 237338 vi PREFACE. motion, and the leading principles of the science of energy, by which Heat becomes related to other forms of motion, are discussed. It may be well to state the basis on which the reason- ing of this part has been founded. It has appeared to the Author that the foundation which involves the smallest amount of assumption is that adopted by Professor W. Thomson, namely the denial of the possibility of a per- petual motion of any kind, and it will be shewn in the sequel that the denial of one form of perpetual motion involves the principle of the ' conservation of energy/ while the denial of another form involves the principle of the ' dissipation of energy/ In our ignorance of the ultimate constitution of matter it would thus appear that both the ' conservation of energy' and the ' degradation or dissipation of energy' should be viewed as principles having very strong claims to recognition, and as increasing these claims every day by the new facts which their employment as instruments of research is constantly bringing to light. A few words with regard to the mode in which the subject of temperature is viewed. Some eminent philosophers are of opinion that our methods of subdividing a range of temperature are to a great extent arbitrary, so that provided we always adhere to the same method we shall not be led into error. Be this as it may, there can be no question that some methods of doing this are much more convenient than others; nay, even that one method, that by the air ther- PREFACE. Vll mometer, enjoys such a pre-eminence of convenience that it may with propriety be termed the proper method of sub- dividing a range of temperature. Starting with the assumption that there is a proper method of measuring temperature, it is shewn near the beginning of this work that even if we are ignorant of this proper method there is yet an advantage in employing an air thermometer. This advantage consists in the fact that we may use any permanent gas we choose for our air ther- mometer, and yet obtain results as nearly as may be identical with one another if all our instruments are read on the same principle ; while, on the other hand, the indications of two thermometers filled with different liquids, and both graduated on the same principle, are not strictly comparable with each other. If we determine to prefer an air ther- mometer we still have to decide on what principle it ought to be read, and, while this principle is indicated at the commencement of the work, the reasons in favour of its adoption are not fully discussed until the end. The author cannot omit the opportunity of acknowledging his obligations to several scientific friends for the suggestions and advice they have kindly given him ; more especially is he indebted to the organizing Secretary of this Series of Works at Oxford for much valuable assistance throughout the book. b 2 TABLE OF CONTENTS. INTRODUCTION. Article Definition of ' Heat* 1-2 Summary of Contents 3~io BOOK I. EFFECTS OF HEAT UPON BODIES. CHAPTER I. Temperature, and its Measurement by Thermometers. Preliminary Definition of Temperature .... 11-13 5 Requirements to be fulfilled by a good Thermometer . 14-15 6 Mercurial Thermometer : Process of Filling . . . " -* . :i .' . 1 6 7 Calibration . ...'.".'. .' I? 8 Determination of Freezing-point v . . .18 9 Determination of Boiling-point . ... 19 10 Graduation . . -. ' . . . . .20 13 Various Scales (with examples) . . . .21 13 Correction for Change of Zero . . . .22 15 Other Sources of Error (with example) . . . 23-25 16 Other Thermometers: Alcohol Thermometer .' . . . . .26 19 Maximum Thermometer . .> . . .27 20 Minimum Thermometer . " . . .28 21 Differential Thermometer . . . . . 29 22 Fluctuation Thermometer 30 23 Other Instruments for Measuring Temperature . .31 24 CONTENTS. IX CHAPTER II. Dilatation of Solids. Article Page Experiment shewing Dilatation . - . V , 3 2 2 4 Dilatation of Uncrystallized Solids : 22 25 Linear Dilatation :-(i) Lavoisier's Method of Measuremer /o it 34 26 (2) Ramsden's Method . - ". 35 26 (3) Pouillet and DanielFs Methods . 36 28 Table . . . ' . . . 37 29 Remarks on Table . . 38 31 Cubical Dilatation : -Method of Finding it (with ex- ample) . . . . 39 32 Table 40 34 Relation of Cubical to Linear Di- latation (Table) . .- ,- f 41 35 Increase of Coefficient of Dilatation with Temperature . . ..4 42 36 Dilatation of Crystals , . . . . * t 43 37 Remarks on Dilatation of Solids . . . . . 44-45 37 CHAPTER III. Dilatation of Liquids. Apparent and Real Dilatation . , . . , : , ,. , ^ 46 39 Real Dilatation Measured : (i) Method by Thermometers . 47 39 (2) Method by Specific Gravity Bottle 48 40 (3) Areometric Method (with example) 49 40 Absolute Dilatation of Mercury . . , ./. , -.^ 50-51 4 1 Table of Dilatation of Mercury ...... 52 44 Dilatation of Water 53 47 Table of Dilatation of Water 54 48 Dilatation of other Liquids (with Table) . ' : 55 49 Remarks on Table . . i . ( ' . f * 56 50 Dilatation of Volatile Liquids . ^ . .- ' ^ . 57 50 Contraction from Boiling Points . . r 58 5i General Conclusions ." :. . . ' . V 59 52 CHAPTER IV. Dilatation of Gases. Boyle's Law . . . . . 60 53 Division of the Subject . . . 61 54 Experiment : Gay Lussac's Law . 62 54 X . CONTENTS. Article Page Relation between Temperature and Pressure of Air of Constant Volume '63 56 Relation between Temperature and Volume of Air of Constant Pressure ...... 64 59 Dilatation of other Gases at Ordinary Pressures 65 60 Dilatation of Gases at Various Pressures . . .66 61 Air Thermometer a Measurer of Temperature . -67 61 CHAPTER V '. Applications of the Laws of Dilatation. Division of Subject 68 65 Standards of Length 69 65 English Standard . . . . . .70 65 French Standard (with Table of Comparison) . .71 67 Standards of Weight 72 68 English Standard 73 68 French Standard (with Table of Comparison) 74 69 Standards of Density (with examples, and weight of a cubic inch of water and specific gravity of mercury) . 75 70 Remarks on the English and French System of Standards .76 71 Effect of Temperature on Measures of Time . . -77 73 Graham's Mercurial Pendulum ..... 78 74 Harrison's Gridiron Pendulum 79 74 Compensation Balance 80 76 Other Applications of the Laws of Dilatation : Breguet's Metallic Thermometer . . . . 81 77 Reduction of Barometric Column (with example) .82 77 Expansion and Contraction of Metals . . -83 78 CHAPTER VI. Change of State. Liquefaction and Solidification. Remarks on Change of State 84-87 80 Passage from the Solid to the Liquid State : a. Fusion . . . . . ... .88 82 Table of Melting Points . . . , . 89 82 Change of Density in Melting . . . -9 83 Latent Heat of Fusion '. Qi 83 Influence of Pressure upon the Melting Point .92 84 Alloys and Fluxes 93 85 . Solution 94 85 Freezing Mixtures (with Table) . . . - 95 8 5 CONTENTS. xi Article Page Influence of Pressure upon Solution . . .96 86 Passage from the Liquid to the Solid State : o. Solidification without Change of Composition . 97 86 Lowering of Freezing Point . ; -'.--'.' . 98 87 Freezing of a Lake . . . . . -99 ^8 Regelation . . ~ ." > . . . loo 89 Probable Explanation of Regelation . -^. 101-105 89 . Crystallization . . ...... . 106 92 Anomalies of Crystallization . . . 107-108 93 CHAPTER VII. Change of State. Production of Vapour and its Condensation. Remarks on the Gaseous State -and Division of Subject 109 94 Vaporization and Sublimation . . . . . .no 95 Vaporization in Vacuo . . . . . .Ill 95 Maximum Vapour Pressure in Vacuo . . . .... 1 1 2 96 Mixtures of Gas and Vapour in a Confined Space . .113 96 Mixed Liquids in a Confined Space . . . , * 114 97 Effect of Chemical Affinity on Vaporization . . .115 97 Tension in Communicating Vessels at Different Tem- peratures . . ' . - .' '.'.'*. .116 98 Distillation . . -. ..* . . . II 7 100 Cold due to Vaporization. Freezing Apparatus . . 118 101 Tension in Communicating Vessels filled with Air .119 104 Various Modes of Vaporization I2O 107 a. Evaporation 12 1 107 /3. Ebullition 122 108 Influence of Pressure on the Boiling Point . .123 1 08 Influence of Nature of Vessel on the Boiling Point . 1 24 no Influence of Substances dissolved on the Boiling Point 125 no Influence of Air dissolved on the Boiling Point . 1 26 1 1 1 Influence of Nature of Liquid on the Boiling Point 127 112 Table of Boiling Points and Specific Gravities .127 112 7. Spheroidal State . . . . . 128-130 113 Vaporization at a very high Temperature (with Table). 131 116 Sublimation . . . .' . . . 132 117 Condensation of Vapours and Gases : Condensation of Vapours . . . . . -133 n8 Condensation of Gases . . - . . -134 Il8 Xll CONTENTS. Article Page Elastic Force and Density of Vapours and Gases . . .135 1 2O a. Pressure of Vapour not in Contact with its own Liquid 136 120 . Pressure of Vapour in Contact with its own Liquid .137 122 Pressure of Aqueous Vapour ... . . 138142 122 Correction for Latitude 143 1 29 Tables of Pressure of Aqueous Vapour . . end of Volume 369 Pressure of other Vapours (with Table) . . . 144 131 Remarks on Vapour Pressure . . . 145-146 132 y. Density of Gases and Vapours (with Table) . . 147 133 Laws of Gaseous Density 148 134 Table of Density of Steam 148 136 Weight of one Litre of the most Important Gases .149 137 5. Hygrometry 150-! 54 J 3 8 Daniell's Dew-point Hygrometer .... 155 141 Regnault's Dew-point Hygrometer . . . 156 141 Wet and Dry Bulb Hygrometer . . . . 157 142 Weight of Vapour in Air. Specific Gravity of Air (with example) 158 144 Correction for Weighing in Air . . . -159 145 CHAPTER VIII. Effect of Heat upon other Properties of Matter. General Remarks 160-161 146 Effect of Temperature on Refraction and Dispersion . . 162 147 Effect of Temperature on the Electrical Properties of Bodies : a. Thermo-electric Currents . . . . .163 148 Thermo-electric Series . . . . .164 149 Thermo-pile 165 149 Thermo-electric Inversions . . . . . 166 153 j8. Pyro-electricity . 167 153 y. Effect of Temperature on the Electric Conductivity of Pure Metals .168 154 of Liquids . .169 155 of Bad Conductors .170 155 Effect of Temperature on Magnetism . .- . . .171 155 Effect of Temperature on Chemical Affinity . . .172 156 Effect of Temperature on other Properties of Matter . . 173 156 CONTENTS. Xlll BOOK II. ON THE LAWS WHICH REGULATE THE DISTRIBUTION OF HEAT THROUGH SPACE. CHAPTER I Radiant Heat. (Preliminary.} Article Page Definition of Radiant Heat .. ... ,'.,-. --.' 174 *59 Radiation takes place in Vacuo . . .'- *75 J ^ Radiation takes place equally on all Sides . . ., 176 160 Radiation takes place with the same Velocity as Light . 177 160 It is capable of passing through certain Substances .178 160 It is probably an Undulatory Motion . . ._ .179 1 " 1 Its Intensity varies inversely as the Square, of the Distance . , . . 180 164 CHAPTER II. Reflection, Refraction, fyc. of Radiant Heat. Division of Subject . . . .. . , . . 181 165 Solar Spectrum 182-183 166 Spectra of Heated Solid Bodies . . . . . 184 168 Questions to be answered . . . . .185 169 Reflection of Heat : Dark Heat is capable of Reflection . . . . 186 169 The Heat of Light is Reflected in the same manner as the Light . . ' . . ... 187 172 Variation of Reflecting Power with Angle of Incidence 1 88 172 Diffuse Reflection of Heat .. ," . . '. 189 172 General Conclusions '.'. . J 9O !73 Refraction of Heat . . t , , , . 191 173 Absorption of Heat . . \ -. , '',.: , .192 175 Polarization of Heat . . . . . . .193 ^77 Concluding Remarks. Probable Identity of Heat and Light 194 179 XIV CONTENTS. CHAPTER III. Theory of Exchanges. Article Page Explanatory 195 181 Apparent Reflection of Cold 196 182 Prevost's Theory . . . . . . .197 183 Chamber of Constant Temperature .... 198 184 Equilibrium of Heat Rays : a. Heat Equilibrium of Surfaces Good Reflectors are Bad Radiators . . . 199 184 Reflected plus Radiated Heat equal to Lamp-black Radiation 200 185 Shape of Enclosure without influence on Stream of Heat 201 186 Laws hold good for every kind of Heat . . 202-203 X 88 General Conclusions 204 190 . Heat Equilibrium of thin Plates Small Radiation because Small Absorption of Rock Salt 205 191 Large Radiation from Glass .... 206-207 191 Selective Radiation from Thin Plates . . 208-209 192 Internal Radiation Defined . . . .210 193 Amount of Internal Radiation . . . 211-217 194 Equilibrium of Light Rays : General Remarks 218-219 198 a. Light Equilibrium of Surfaces Small Light from Polished Metal and White Plate .220 199 j8. Light Equilibrium of Thin Plates Small Light from Transparent Glass . . .221 200 Red Glass gives out Greenish Light . . .222 201 Tourmaline radiates Light partly Polarized . .223 201 Coloured Glasses lose their Colour in the Fire . 224 203 Foucault and KirchhoiFs Experiments . . .225 203 Concluding Remarks. Analogy between Light and Sound . 226 204 CONTENTS. XV CHAPTER IV. Radiation at Different Temperatures. Article Page Stream of Radiant Heat depends upon Temperature . 227 205 It is best represented by Radiation from Lamp-black . 228 206 Velocity of Cooling ; Variation with Temperature of QUAN- TITY of Radiation : Newton's Law ,22-9 207 Dulong and Petit's Experiments .... 230234 207 Absolute Measure of Radiation 235 213 Variation with Temperature of QUALITY of Heat : From a Lamp-black Surface 236 214 Sensitiveness of the Eye to Different Rays . . .237 215 Radiation of a Particle; Radiation of Gases : Preliminary Remarks 238 216 Laws of Gaseous Radiation 239 217 Practical Importance of these Laws .... 240 2l8. Constitution of Sun and Stars 241 219 CHAPTER V. Further Remarks on Absorption. Division of Subject . . . . : ' . .. . 242 222 Absorption of Dark Heat by Different Bodies : Melloni's Table 243 222 Remarks on this Table 244 224 Professor Tyndall's Experiments .... 245 224 Remarks on these Experiments . . . . 246 225 Absorption of Light by Different Bodies : Selective Absorption of Bodies for Light . . : . 247 226 Metallic Reflection 248 227 Certain Practical Consequences : Globe with Athermanous Envelope . '.--. . 249 228 Case of our own Globe. Importance of Aqueous Vapour 250 2 30 Rapid Refrigeration in Central Asia, &c. . . .251 230 Formation of Dew 252 231 Artificial Formation of Ice . . . . 2 53 2 3 2 XVI CONTENTS. CHAPTER VI. Radiant Heat. Phosphorescence and Fluorescence. Article Page Definition of Phosphorescence 254 232 Duration of Effect. Phosphoroscope . . . . 255 233 Definition of Fluorescence . . . . . 256 234 Explanation of Professor Stokes 357 235 Laws of this Phenomenon . . . . . .258 235 Likeness between Phosphorescence and Fluorescence .259 236 Practical Advantages derived from these Phenomena .260 237 CHAPTER VII. Conduction of Heat. Definition of Conduction, and Preliminary Remarks 261263 238 Conduction of Heat in Homogeneous Solids : Experiment 264 240 Flow of Heat across a Wall .... 265-269 240 Definition of Thermal Conductivity . . . .270 243 Flow of Heat along a Bar. Principal Forbes' Experi- ments 271-275 244 Table of Relative Thermal Conductivity of Metals . 276 249 Variation of Thermal Conductivity with Temperature (with Table) 277 250 Similarity of Bodies as regards their Thermal and Elec- tric Conductivity (with Table) . . . .278 251 Difference between Transmission of Heat and Transmis- sion of Temperature . 279 252 Safety-lamp 280 253 Conduction of Heat in Non-homogeneous Solids and Crystals 281 254 Conductivity of Fluids 282 255 CHAPTER VIII. Convection of Heat. Convection in Liquids : Experiment . . ,-. . . . . . 283 256 Convection depends on Dilatation and on the Force of Gravity . . ... ,'..,- . . -, 284 258 Convection in Gases , .285 258 Trade Winds, &c 286 258 Law of Cooling due to a Gas (with example) , , 287 260 CONTENTS. xvii CHAPTER IX. Specific Heat. Article Page Definition . . .-.<' .. . '' 288 263 Methods of Measuring Specific Heat : (1) Method by Mixture (with example) . . . 289 264 (2) Method by Fusion of Ice . , . . . 290 265 (3) Method by Cooling . . . , .- ; . . 291 266 Specific Heat of Solids : Regnault's Experiments . . . . . 292 266 Rise with Temperature (with Tables) . .' . . 293 267 Circumstances which influence the Specific Heat of Solids (with Table) 294 268 Specific Heat of Liquids : Regnault's Experiments. General Results . . . 295 269 Variation with Temperature of Specific Heat of Liquids 296 270 Specific Heat of Water at various Temperatures . . 296 270 Specific Heat of Gases : Division of the Subject. Regnault's Experiments . 297 270 Results of Regnault's Experiments .... 298 274 Table of Specific Heat of Gases under Constant Pressure 299 274 Influence of State on Specific Heat (with Table) . . 300 275 Atomic Heat : Atomic Heat of Simple Bodies (with Table) . .301 276 Atomic Heat of Compound Bodies (with Table) . . 302 277 CHAPTER X. Latent Heat. Preliminary Remarks . . . . ., . 303 278 Latent Heat of Liquefaction : Latent Heat of Water . . ... 304 35 279 Person's Experiments on Latent Heat of Water . . 306 281 Latent Heat of other Liquids (with Table) . . . 307 282 Latent Heat of Vaporization : Latent Heat of Steam (with Table) .... 308 283 Latent Heat of other Vapours (with Table). . . 309 285 XV111 CONTENTS. BOOK III. ON THE NATURE OF HEAT, ITS SOURCES, AND CONNECTION WITH OTHER PROPERTIES OF MATTER. CHAPTER I. Remarks on Energy. (Historical and Preliminary.} Article Page Introduction 310 287 Perpetual Motion 311 287 Definition of Energy (i) Kinetic Energy . . 312-314 289 (2) Potential Energy . . 315-316 292 Functions of a Machine . . . . . . 317 294 Conversion of Mechanical Energy into Heat . 318-319 294 Conversion of Heat into Mechanical Energy . . 320 296 Various Principles of the Science of Energy . .321 296 Various Forms of Energy 322-323 297 List of Transmutations of Energy . . . 324-325 2 99 CHAPTER II. Relation between Heat and Mechanical Effect. First Law of Thermo-Dynamics : Davy's and Rumford's Experiments . . . .326 301 Joule's Experiments (i) Fluid Friction . . .327 302 (2) Magneto-Electricity . . 328 304 Mechanical Equivalent of Heat defined . . .328 304 Joule's Experiments (3) Condensation of Gases . 3 2 9~ 33 1 35 Specific Heat of Gas of Constant Volume . . . 332 307 Second Law of Thermo-Dynamics : Reversible Engines defined, &c. . . . 333~334 31 Reversible Engines of Infinitely Small Range . 335-34 3 12 Carnot's Function 341 316 Probable Form of this Function . . . 34 2-343 S 1 ^ Perfect Engines of Great Range . . . 344-345 318 Work Done by Perfect Engines .... 346 320 Absolute Zero of Temperature 347 321 CONTENTS. XIX CHAPTER 1 1 1 .History of Heat Engines. Article Page Preliminary . . . . '-v- . . 34$ 321 Hero's Engine . . . . '. ' * 349 322 Blasco de Garay . . . .' ; . . 350 323 Porta, De Caus, and Worcester . . : - . < . 351 323 Papin , ifi . . 35 2 3 2 4 Savery [ .' . 353 324 Newcomen . . . . . . . -354 3 2 5 Watt. Separate Condensation 355 326 Air Pump 356 327 Double Action 357 328 Expansive Working 358 328 Table of Performance of Engines . . . . 359 329 Definition of Horse Power . . . . . 360 329 Economy of Heat . . . . . . .361 330 Locomotive Engines 362 330 CHAPTER IV. Connection between Heat and other Forms of Energy. Connection between Heat and Electricity in Motion : Conversion of Electricity in Motion into Heat (with example). . . . . .- 363-366 331 Conversion of Heat into Electricity in Motion . .367 335 Pel tiei's Experiment . . . . , . .. 367 335 Connection between Heat and Molecular Potential Energy : Latent Heat 368 336 Gradual Change of Molecular State . . . .369 338 Connection between Heat and the Potential Energy of Chemical Separation : a. Transmutation of the Potential Energy of Chemical Separation into Heat .... 370-37* 339 Andrews' Experiments 372 341 Tables of Heat developed by Combustion . . 373 342 Metallic Precipitates 374 343 Nature of Flame . 375 344 Heat Absorbed when Salts Dissolve, and the converse 376 345 Heat Evolved during the Solution of Gases . -377 345 ,3. Transmutation of Heat into the Potential Energy of Chemical Separation , , : ' . . . 378 346 Connection between Heat and the Potential Energy of Elec- trical Separation 379 347 XX CONTENTS. CHAPTER V. Dissipation of Energy. Sources of Energy. Concluding Problems. Dissipation of Energy : ArtMe Pas e Statement 380-384 347 Available Energy of a Hot Body .... 385 350 Universal Dissipation of Energy .... 386 351 Medium Pervading Space 387 352 Sources of Energy : o. List of Sources 388 354 Fuel and Food 389 354 Head of Water 390 356 Tidal Energy .391 356 Native Sulphur, &c 392 357 Air and Water in Motion 393 357 Unequal Temperature of Globe . . . . 394 357 List of Really Serviceable Sources of Energy . . 395 357 Coal (probable exhaustion of) .... 396 357 )8. The Sun the Great Dispenser of Energy . . 397 358 Actinometric Observations 398 359 Origin of the Sun's Heat 399 361 Concluding Problems 400 362 Effect of Pressure on Freezing-point of Water . .401 362 Temperature 402-403 364 Tables of Pressure of Aqueous Vapour at various Temperatures: Table I. Shewing the Elastic Force of Aqueous Vapour in inches of Mercury at the Latitude 53 21' for each degree Fahr. from 30 to 432. . . . 369 Table II. Shewing the Elastic Force of Aqueous Vapour in inches of Mercury at the Latitude 53 21' from o to 1 00 Fahr. for every two-tenths o a degree . . 373 Table III. Shewing the Elastic Force of Aqueous Vapour in millimetres of Mercury at the Latitude of Paris (48 50') for each degree Centigrade from 32C to + 23oC 377 INTRODUCTION. 1. The word 'Heat' is used in the following treatise to denote that agent which produces a certain well-known sensation when applied to the human body. 2. But this sensation while so familiar to us that every one must immediately recognise what agent is meant when the term Heat is used, is yet not sufficiently definite or constant to afford us the means of accurately measuring the amount of heat which a body possesses. The same substance may at the same time appear warm to one indi- vidual and cold to another ; nay, it may even be pronounced warm by one of our hands and cold by the other. Our judgment with regard to the amount of heat possessed by the substance in question is thus found to depend upon the state of our bodies, and as this changes from time to time we cannot therefore make use of our sensations as a means of measuring heat. 3. In the study of this subject it is thus of primary importance to become acquainted with some instrument by the aid of which the state of bodies with regard to heat may be accurately determined. The Thermometer fulfils this requirement, and a description of it will therefore form the commencement of this treatise. 2 INTRODUCftpN. 4. "When the 'Thermometer has been described the various effects produced in bodies by the presence of heat may next with advantage be studied. Such effects are change of volume ; of condition ; of hardness ; chemical change ; with other effects which will afterwards be mentioned. 5. The laws which regulate the distribution of heat will next be considered, and under this head it will be necessary to recognise two distinct modes of conveyance of this agent from one body to another. Every one is familiar with the fact that the contact of a cold body with a hot one, whether solid, liquid, or gaseous, will cause the latter to part with some of its heat. But this is not the only way by which heat may reach us ; for we derive a very considerable amount from the sun, although this luminary is at a great distance from the earth, while the intervening space does not contain that gross form of matter which serves to convey heat by contact. We are thus taught that a hot body parts with its heat in two ways, (1) By contact with a cold body ; (2) By radiation through space. And we believe, moreover, that radiant heat traverses space with the enormous velocity of 190,000 miles per second. 6. We have thus the means of making a very convenient and easily perceived classification of the modes in which Heat exhibits itself to us. There is, in the first place, what we may call absorbed heat, which resides in a hot body, and often remains in it for a considerable time ; and we have, in the next place, radiant heat, which is ' heat in the act of passing through space with a very great velocity. 7. In treating of the laws which regulate the distribution of heat this distinction may with propriety be observed, and INTR OD UC TION. 3 this part of the subject will thus divide itself into two. It will be desirable to consider, in the first place, radiant heat its nature, and the laws which regulate its distri- bution; and then to consider the laws which regulate the distribution of absorbed heat, while under this last heading the capacity of bodies for heat will be brought forward. 8. In treating of radiant heat theoretical views will for the first time be introduced. It is well known that there have been two distinct theories regarding the nature of Heat. In one of these it is viewed as a substance which insinuates itself between the particles of a hot body, while in the other it is regarded as a species of motion taking place amongst these particles. Such views could not well be introduced at an earlier stage of the work, since the more prominent effects of heat upon bodies form a set of phenomena that are capable of being explained tolerably well by either hypothesis. They are therefore somewhat unsuitable as tests of a theory, while, on the other hand, they are of extreme importance as facts. But the study of radiant heat enables us to pronounce with a near approach to certainty that this influence is not a substance ejected from a hot body, but rather a description of undulatory motion transmitted through a medium per- vading all space. 9. It would appear to follow, as a corollary from this view, that ordinary heat into which radiant heat is trans- formed when absorbed must also be a species of motion, and this idea will be abundantly confirmed in the next part of the subject, where the various sources of heat will be treated of, and the nature of this agent as well as its con- nexion with other properties of matter fully discussed. 10. Lastly, this treatise will contain throughout notices of some of the most important practical applications of the laws of Heat, and also of certain terrestrial and cosmical adaptations in which these laws play a very important part. B 2 4 INTRODUCTION. It will be observed throughout that the term Caloric is avoided as much as possible, since this term has come to be associated with that theory which regards heat as a sub- stance and not as a species of motion. BOOK I. EFFECTS OF HEAT UPON BODIES. CHAPTER I. Temperature, and its measurement by Thermometers. DEFINITION OF TEMPERATURE. 11. The temperature of a body may be defined to be its state with respect to sensible heat. When the amount of sensible heat in a body increases, its temperature is said to rise, and when this diminishes its temperature is said to fall. It is expedient to discuss at the outset certain fun- damental principles which underlie all measurements of temperature. 12. If there be two substances, as for instance water and mercury, in such a condition that when brought intimately into contact with one another and shaken together neither of them changes its state with respect to heat, then these two bodies may be said to be in a state of equilibrium of temperature with each other. Suppose now that the mercury is in a similar state with respect to a third substance, oil. We have thus the water in equilibrium of temperature with the mercury and the mercury in equilibrium of temperature with the oil. Now we know, as the result of experience, that we shall also have the water in equilibrium of temperature with the oil. In fine, if a series of bodies be in equilibrium of temperature with each other in any one order they will be so in any other order; and no matter how they are brought 6 TEMPERATURE, AND ITS together or mixed up with one another, they will always retain unchanged their state with respect to heat. All such bodies are said to be of the same temperature. But if when the water and the mercury are brought together the water parts with some of its heat to the mercury, then it is said to be of a higher temperature than the mercury ; and if, on the other hand, the water receives heat from the mercury, then it is said to be of a lower temperature than the mercury. 13. It will be inferred from what we have said that if two bodies of different temperature be intimately associated with one another they will both at length attain one common temperature. Let us now suppose that we have a large mass of liquid whose temperature we wish to measure by means of a thermometer. Strictly speaking, when the thermometer and the liquid are brought intimately together, a common tempera- ture will be attained, but if the mass of the liquid be very much greater than that of the thermometer the former will not be appreciably changed in temperature by the immersion in it of the latter, and the result will be that the thermometer will denote with sufficient accuracy the temperature of the liquid only it is necessary that this instrument be very small. But if the temperature of the liquid be kept constantly recruited by some natural process, as for instance that of boiling, the thermometer will in such a case, whatever be its size, at length attain the temperature of the boiling liquid in which it is immersed; but a small thermometer will attain this temperature sooner than a large one. 14. Requirements to be fulfilled by a good Thermo- meter. Having stated these facts, let us now point out the requirements which an instrument for measuring temperature may be expected to fulfil, ist, it ought to be of small size and easily portable. 2nd, it ought always to give the same MEASUREMENT BY THERMOMETERS. 7 indication for the same temperature, or to be capable of doing so by a simple correction. 3rd, it ought to do some- thing more than merely denote that one body is hotter or colder than another. For the difference between two tem- peratures, such as the freezing and the boiling points of water, is one which we conceive to be capable of accurate subdivision into any number of equal parts, which form as it were successive equal steps by which we may mount from the lower to the higher temperature. This last requirement is the most difficult one, for it implies not only a knowledge of the agent Heat, but also of the changes which it produces upon bodies, since we must evidently make use of some one of these changes in the construction of our instrument for measuring temperature. While a mercurial thermometer may probably be so made as to fulfil the first and second of these requirements, it is an air thermometer which will best satisfy the third; but the reasons which lead us to suppose that this instrument gives us the means of measuring temperature with great accuracy cannot well be discussed at the outset of this work. These will be given hereafter : in the meantime, let us take it for granted that an air thermometer does really fulfil this require- ment, and refer our readers for a description of this instru- ment to our chapter on the dilatation of gases. 15. But while an air thermometer gives a very correct indication of temperature, it is nevertheless an instrument difficult of construction and awkward in use: it ought therefore to be employed rather as a standard of reference, by means of which the errors peculiar to some other instrument of easy construction and simple form may be determined. MERCURIAL THERMOMETER. 16. An instrument of this kind is found in the mer- curial thermometer, which is constructed upon the principle 8 that mercury when heated expands very much more than glass. In making a mercurial thermometer a bulb is first blown at one extremity of a tube of glass having a capillary bore, the other end of the tube being open to the atmosphere. The bulb is then heated so as to drive out some of the air which it contains, and the open end of the tube is inserted into a basin of pure mercury. As the bulb begins to cool and the pressure of the air within it diminishes, part of this mercury will be driven up the bore into the bulb. The mercury is then boiled, and the mercurial vapour drives away any air or moisture that may have adhered to the tube. While the instrument is hot and full of the vapour of mercury its extremity is once more plunged into the basin, by which means, on condensation of the vapour, the bulb and tube will be filled with mercury. When the tube is full of mercury it is hermetically sealed, and when the instrument has cooled the mercury ought to fill the bulb and part of the stem, the other part being empty. If now the bulb of this instrument be heated the glass envelope will expand, and also the mercury with which it is filled ; but the mercury will expand much more than the glass envelope, and in con- sequence the mercurial column will rise in the capillary tube. If the bore be fine enough, a considerable rise may thus be produced even when there is only a small expansion of the mercury, and by this means a very great amount of delicacy may be given to the instrument. 17. Calibration of the tube. If the instrument is to be as accurate as possible, it is necessary to know the relative diameter of the bore at different parts of its length, since this is always variable even in the best tubes. To accomplish this the tube is made by the glass-blower in such a way that by a simple mechanical contrivance a small column of mercury, occupying the length of about MEASUREMENT BY THERMOMETERS. 9 one-third of an inch in the bore, may be detached from the main body of the fluid. This column is then made to travel from the one extremity of the tube to the other, and its length is measured by a microscope at each short stage of its progress. It is obvious that this column will be long where the bore is narrow and short where it is wide, and that by this means we may obtain the relative diameter of the bore in different parts of the tube. The detached column having served its purpose is now reunited to the main body of the mercury. It will be afterwards seen (Art. 20) in what manner the information thus obtained is made use of. 18. Determination of the fixed points. The freezing point. Our object in constructing a thermometer presup- poses the existence of at least two fixed points of temperature. The two universally adopted are the freezing and the boiling points of water. Suppose that a substance ascends from the lower to the upper of these temperatures through a certain number of equal stages or degrees, it is the office of the thermometer to indicate these. In order to determine the lower fixed point, a wooden box is perforated in the bottom with a few holes to permit drainage, and placed in a room whose temperature is above the freezing point of water. It is then filled with snow or pounded ice in a melting state, and it has been ascertained that the temperature of this melting ice is under ordinary circumstances absolutely constant. The thermometer is now placed vertically in this mixture, the ice being heaped about the stem, and is so left for a quarter of an hour, or until the mercury has become stationary. The tube is then marked with a scratch at the termination of the mercurial column, and the lowest of the two points is thus determined. Presuming that Fahrenheit's scale is to be employed, this point will denote 32. 10 TEMPERATURE, AND ITS 19. The boiling point. The next process consists in determining the boiling point of water. This, unlike the freezing point, is not strictly constant, for the temperature of steam in contact with water depends upon the pressure under which it exists. It had been observed by Gay Lussac that water boils under the same pressure at slightly different temperatures in different vessels ; but Rudberg afterwards found that the nature of the containing vessel altered only the temperature of the water and not that of the steam. It is therefore in steam, not water, that a thermometer ought to be plunged in order to have its upper point determined. Hence also if steam escape from an open vessel containing water into the air, the temperature of the steam, which depends upon the pressure under which the steam exists, will therefore depend upon the atmospheric pressure, since this must be the same as that of the steam. The temperature of the steam of water boiling in an open vessel will therefore vary with the barometer; but if we know the law of this variation we can make allowance for it in graduating our thermometer. The Commissioners appointed by the British Government to construct standard weights and measures, and the Kew Committee of the British Association, have both agreed that the upper point of a thermometer graduated according to Fahrenheit's scale, or that adopted in this country, shall be taken to represent at London the temperature of steam, at the pressure of 29.905 inches of mercury reduced to the freezing point. This is therefore the true meaning of 2 12 Fahrenheit, and the temperature of steam at other pressures may be found from the following table. MEASUREMENT BY THERMOMETERS. Temperature of steam at different pressures. Pressure in Tempera- inches of ture. mercury at 32Fahr. Pressure in Tempera- inches of ture. mercury at 32Fahr. Pressure in Tempera- inches of ture. mercury at 32Fahr. 211.0 29.315 2II.I 29.374 211. 2 29.432 2II.3 29.491 2II.4 29.550 2II.5 29.609 2H.6 29.668 211.7 29-727 211.8 29.786 211.9 2 9-845 212.0 29.905 212. 1 29.964 212.2 30.024 212.3 30-0 8 3 212.4 30.143 212.5 30-203 212.6 30.263 212.7 30.323 212.8 30.3 8 4 212.9 30.444 We are thus furnished with the means of determining the higher point. Let the instrument be immersed in steam arising from boiling water, mark off as before the termination of the mercurial column, reading the barometer at the same moment. If the pressure of the atmosphere be 29.905 inches, this point will denote 212; and for any other pressure the true value of the mark may be found from the above table. In performing this operation it will be found most conve- nient to employ Regnault's apparatus (see page 12). The arrangement will best be perceived from Fig. 2, which repre- sents the interior of the instrument. A is a thermometer having its bulb a little above E, the level of the boiling water. The course which the steam is forced to take is denoted by the arrow-heads. It is thus seen that the steam must pass up along the thermometer tube and down again, until finally it leaves the apparatus by the orifice C. The whole of the tube of the instrument is thus thoroughly surrounded by steam, and by a cylinder of the temperature of the steam. D is a bent glass tube, open to the atmo- sphere, and containing a little water, which shews by a difference of level in the two limbs if the pressure of the steam in the interior is greater than that of the atmo- sphere without. It has been ascertained that, if the orifice 12 TEMPERATURE, AND ITS is sufficiently wide, this difference is too small to affect the temperature of the thermometer, and thus the gauge D may be dispensed with. Fig. i. Fig. 2. The thermometer is inserted through a closely fitting slit in a thick piece of india-rubber which rests upon the top of the apparatus, and the stem is lowered until the column of mercury just appears above the india-rubber ; and thus nearly all the column as well as the bulb is exposed to the vapour of boiling water. This apparatus is generally formed of copper, and distilled water should if possible be used. It ought also to be noted that in marking off the MEASUREMENT BY THERMOMETERS. 13 points the lower or freezing point should always be deter- mined first ; the reason for this will be afterwards given. 20. Graduation. Fahrenheit's scale. The relative diameter of the bore at different parts of the tube having now been determined by calibration (Art. 17), and the two fixed points marked, it is easy to graduate the instrument. If the scale is to be that of Fahrenheit, the lower point is called 32 and the upper point (provided the atmospheric pressure be 29.905 inches) 212. There are thus 180 divisions between the two points, and these are marked upon the tube in the following manner. The whole instrument is covered over with wax sufficiently thin to allow the two marks (previously blackened) to be visible, and a needle attached to a dividing engine scratches the graduations in the wax. The thermometer is then exposed to hydrofluoric acid or its vapour, which attacks the glass where the wax has been scratched off. The length of each degree is regulated by the previously determined diameter of the bore in such a manner that the internal capacity of the tube between the two marks is divided into 180 equal parts. The graduation is generally extended below the freezing point, and sometimes above the boiling point. In this thermometer a temperature 32 below the freezing point is termed zero, while one ten de- grees lower is called minus 10, or 10 below zero, and so on. 21. Other scales. Besides Fahrenheit's scale there are two others, those of Celsius and Reaumur. The former of these is also called Centigrade, and is used throughout France, and the latter very generally in Germany. In the Centigrade thermometer the freezing point of water is termed o, or zero, while the boiling point is reckoned equal to 100. A degree Centigrade is therefore greater than a degree Fahrenheit in the proportion of nine to five. The boiling point in this thermometer, or 100, is defined to be the temperature of steam under the barometric pressure 14 TEMPERATURE, AND ITS of 760 millimetres, or 29.922 inches of mercury reduced to the freezing point of water at the latitude of Paris. This is slightly different from the corresponding point, or 212, in Fahrenheit's scale, which, as we have seen, denotes the temperature of steam under the pressure of 29.905 inches of mercury reduced to 32 at the latitude of Lon- don. It must, however, be borne in mind that the force of gravity, and therefore the absolute pressure towards the earth of the same mass of matter, is somewhat greater in London than at Paris, so that 29.922 inches of mercury in Paris are equal in absolute pressure to 29.914 inches at London (see Art. 143). This still leaves a slight difference between the absolute pressure of the steam in the two cases, and hence the upper points of these two instruments will not quite correspond in temperature; but this difference is so very small that for ordinary purposes it may be neglected. To reduce Fahrenheit to Centigrade the following formula is made use of, C = (F 32) -; while to reduce Centigrade to Fahrenheit we have F = +32. o Thus, were it required to find what degree Centigrade corresponds to 77Fahr., we should proceed in the following manner. Subtracting 32 from 77 we find that this tempera- ture is 45 above the freezing point, or Centigrade zero, and taking J- of 45, since Centigrade degrees are greater than those of Fahrenheit in this proportion, we find that 25 Cent, corresponds to 77 Fahr. Again, were it required to find what degree Centigrade corresponds to 3 8. 2 Fahr., we should have, as above C = (- 38.2 - 32) 5 or C = - 70.2 x ? = _ 39. In the scale of Reaumur the distance between the freezing and boiling point is divided into 80 parts, and the boiling MEASUREMENT BY THERMOMETERS. 15 point is defined to be the temperature of steam under the pressure of 760 millimetres of mercury, the force of gravity being that which corresponds to latitude 45. To reduce Fahrenheit to Reaumur we have therefore the following expression, R = (F 32) -; while to reduce Reaumur to Fahrenheit we have F = (-32. 4 22. Correction for change of zero. It is found that thermometers are liable to an alteration of their zero points, especially when the bulb has been filled not long before graduation. This displacement is of the following nature. Immediately after graduation 32 will of course denote the temperature of melting ice, but when some time has elapsed a thermometer placed in melting ice will no longer give this reading, but one somewhat higher, perhaps 32.4 or 32.5. When an instrument has been graduated shortly after the filling of the bulb, this displacement may in the course of years amount to nearly 2 Fahr., but it is believed that this is the extreme limit of the change. But if the bulb has been kept for some time before graduation, and has also been well annealed, the change is much less : nevertheless it may possibly amount in the course of years to six or seven tenths of a degree. Besides this progressive and permanent change there is also a temporary one, produced by heating and suddenly cooling the instrument. For instance, if a thermo- meter have first of all its freezing point determined by melting ice, if it then be plunged into boiling water, then suddenly withdrawn, and finally plunged again into ice, the freezing point will be found to have changed the instrument may now read 31.8, and it will not recover its true reading until ten days or a fortnight have elapsed. This is the reason why the freezing point is always marked off first in constructing the instrument. 1 6 TEMPERATURE, AND ITS To correct for change of zero the thermometer ought to be plunged from time to time into melting ice, and its reading noted. The amount of alteration thus becomes known, and the requisite correction may be applied, which is of course constant throughout the scale. 23. Other sources of error. If a thermometer have its fixed points determined in a vertical position it must always be used in this position: in like manner if these points are determined in a horizontal position of the instru- ment, then it must always be used horizontally. The reason of this is that for the same temperature the same instrument will give a higher reading in a horizontal than in a vertical position, since in the latter the hydrostatic pressure of the column of mercury will tend not only to compress the particles of mercury into less volume, but also to enlarge the capacity of the bulb. For a similar reason the reading of an unprotected thermometer in vacuo will be different from its reading in air. 24. Again, when the volume of mercury in the stem of a thermometer is exposed to a temperature different from that of the bulb, a correction must likewise be made on this account. For instance, if the bulb and the column of mercury up to freezing-point mark have the temperature of boiling water, while the remainder of the column is exposed to the atmosphere, which we may imagine to be at 32, then the instrument will not indicate 212. It would have done so had the whole of the mercury been heated up to the boiling point, but this is not the case, for nearly 180 degrees, or the distance between the freezing-point mark and the extremity of the column, is exposed to the atmosphere, and may be taken to have the same temperature as it has. In order to find the correction which we ought to apply, MEASUREMENT BY THERMOMETERS. 17 let us denote by unity the whole volume of the mercury when it is all at the temperature 32: unity will therefore also denote the internal capacity at this temperature of the glass envelope up to freezing-point mark. Now it will be afterwards shewn (Art. 52) that this mercury when raised to 212 will have the volume 1.0182 nearly, and also (Art. 40) we may perhaps suppose that the internal capacity of the glass up to freezing-point mark will have, when raised to 212, the volume 1.0026: this however depends upon the nature of the glass. Hence a volume of mercury equal to 1.0182 1.0026, or .0156, will exist in the tube above the freezing-point mark provided that the whole column of mercury be heated up to 212; and it will under these circumstances occupy 180 degrees of the bore. The ques- tion to be answered is, how many degrees of the bore will this portion of mercury occupy when both it and the tube con- taining it are at 32. Evidently the absolute volume of this portion of mercury at 32 will be .0156 x = .01532. Hence if we imagine the bore of the tube to preserve a constant volume for all temperatures, the rise may easily be found. For if the volume .0156 occupy 180 divisions, the .01532 volume .01532 will occupy 180 x ^- or 176.8 divisions. But the bore of the tube in which this rise takes place does not preserve a constant volume throughout, but, being only at 32, is really of smaller capacity than it was at 212, in the ratio of i to 1.0026 : the rise of i76.8 will therefore have to be increased in this proportion, and will become 1 7 7. 2, or the mercury will indicate 2 09. 2 as the boiling point of water; a correction of -f 2.8 must therefore be applied. This example will convey to the reader sufficiently well the method to be employed in finding this correction, but c 1 8 TEMPERATURE, AND ITS it ought to be borne in mind that it is much better when practicable to avoid the necessity for it, by exposing the whole column of mercury as well as the bulb to the influence of the temperature which we wish to estimate. 25. Lastly, even when a mercurial thermometer has been constructed with the greatest accuracy after the method indicated in the preceding articles, so that the freezing point is denoted by 32 and the boiling point by 212, while each degree denotes precisely the iSoth part of the capacity of the bore between these two points, it does not follow that the instrument will give an intermediate temperature with absolute exactness. For, in the first place, it does not follow that the expansion in volume of the mercury above that of the glass envelope up to freezing-point mark for a true rise of 90 must be precisely half of its expansion for a true rise of 180. In the next place, it ought to be borne in mind that the rise of 90 takes place in a bore of which the temperature is only 122, and of which therefore the capacity is smaller than when the temperature is 212, in the proportion of 1.0013 to 1.0026. Both of these circumstances will introduce errors, and Regnault has found that when the graduation is extended much above 212, the difference between the mercurial and the standard air thermometer becomes very considerable at high temperatures, and also varies with the nature of the glass. But between 32 and 212, and for a range extending not too far beyond these points, a mercurial thermometer well graduated may be considered to be a tolerably good though not a strictly accurate instrument. Since the best thermometers made in this country are all formed of the same kind of glass, it would be desirable that a few of these should be compared with an air thermometer at temperatures between 32 and 212. The writer of this MEASUREMENT BY THERMOMETERS. 19 work hopes that he may ultimately be able to make this comparison. OTHER THERMOMETERS. 26. Alcohol Thermometer. It is well known that mercury freezes at about 38 Fahr., while it boils at about 660 Fahr. A mercurial thermometer cannot therefore be used below the former point or above the latter. But while the superior limit of its accurate employment is considerably below the higher temperature, its indications may probably be relied upon very nearly to the point at which the mercury freezes. It is, however, often desirable to register still lower temperatures, and in order to do so a thermometer filled with absolute alcohol is employed. Such an instrument is not capable of being constructed with the same amount of exact- ness as a mercurial thermometer ; but yet if it be carefully made, and used with caution, very good results may be ob- tained. An alcohol thermometer ought before graduation to be marked off at 32, and at some higher temperature by comparison with a mercurial standard thermometer. The freezing point of mercury ought also, if possible, to be made use of as a fixed point ; and it has been ascertained that this, like the freezing point of water, is of constant temperature, its true value, on Fahrenheit's scale, being 37.9. An alcohol thermometer may be used for very low temperatures, since this fluid has not yet been frozen. When a very accurate determination is desired, this ther- mometer should be kept in a vertical position, bulb down- wards, for some time before it is read. The reason of this is that alcohol, unlike mercury, wets the capillary glass tube which contains it, and is also very volatile : great care ought therefore to be taken that there is no liquid above the main column, whether condensed or adhering to the sides of the tube. c 2 20 27. Maximum and Minimum Thermometers. Maxi- mum. It is often of importance to know not merely the present temperature, but likewise the highest or lowest point to which an instrument has been exposed. Meteorologists, for instance, should be able to register every evening and morning the highest and lowest temperatures of the atmo- sphere. This, when not accomplished by a continuous pho- tographic registration of temperature, is done by maximum and minimum thermometers. In Rutherford's maximum thermometer the stem is placed in a horizontal position, and the bore contains a small index made of iron or graphite, which the mercury pushes before it when it expands through increase of temperature ; but when it retreats this index is left behind, since there is no cohesion between it and the mercury. In Professor Phillips' maximum thermometer this index is part of the mercurial column itself, which, as in Fig. 3, is separated from the main body of the Fig. 3- fluid by a little air. When the mercury expands, the elastic force of the air pushes the index on before it; but this is kept in its position when the mercury again contracts. By this arrangement there is no risk of the index soiling the mercury or becoming entangled with it. It has also been found that when the bore is sufficiently narrow the instrument may be used in a vertical position, bulb downwards, and it is thus of service in chemical operations. Both of these maximum thermometers when read must be reset by shaking the index down towards the mercurial column as far as it will go. Negretti and Zambra's maximum thermometer is exhibited in Fig. 4. When used the stem of this instrument ought to be inclined downwards. The bore is nearly choked at A by MEASUREMENT BY THERMOMETERS. 21 means of a bit of enamel or glass. When the mercury ex- pands, it does so with sufficient force to push its way past this obstruction ; but when it contracts, that part of the column past the obstruction is kept there, and the contraction takes Fig. 4 . place by the mercury to the left of A withdrawing into the bulb. It does not matter if the column past the obstruction go down to the bottom of the tube, for when the instrument is read it is gently tilted up until this detached column flows back to the obstruction, where it is arrested, and the end of the column will then denote the maximum temperature. In resetting the instrument it is necessary to shake the detached column past the obstruction, in order to fill up the vacancy left by the contraction of the fluid after the maximum had been reached. 28. Minimum. In Rutherford's minimum thermometer alcohol is used, and a small glass index is immersed in the column of this fluid. When the instrument has been set this index is at the termination of the column which is kept in a horizontal position. Now should the temperature rise and the alcohol expand, it will flow past the index ; but should the alcohol contract, it carries the index with it, for the fluid does not readily permit of its concave capillary surface being broken. The minimum temperature is thus registered. In order to overcome the objection attached to the use of 22 TEMPERATURE, AND ITS alcohol, L. Casella has lately proposed a mercurial minimum thermometer. The principle of this instrument will be un- derstood from Fig. 5. Its peculiarity consists in a side chamber, AB, the bore of which at A becomes smaller very abruptly, and afterwards swells into a pear-shaped termination. But even after it has been abruptly nar- rowed this bore is still much wider than that of the main tube CD. When the instrument is f JOT, * set, the mercury fills the side chamber as far as the abrupt termination A, but the pear-shaped 'vessel is left empty. Suppose now the tem- perature to rise instead of the column in the main tube moving, the rise will take place by the mercury at A flowing into the pear-shaped vessel : the reason of this probably being that the bore is here wider than that of the main tube, and there is consequently less resistance to the movement of the fluid. Suppose, next, that the temperature falls the fluid in the pear-shaped vessel will first contract, but when the mercury has reached A, or the point at which the instrument was originally set, the effect produced by the flat surface at A will prevent the mercury receding farther, and the contraction will now take place in the main tube. Thus any fall below the temperature of setting takes place in the main tube, while any rise takes place in the side chamber; and hence the instrument serves as a mini- mum thermometer. A comparison at Kew Observatory has shewn that the indication of such an instrument agrees very nearly with that of a Rutherford's minimum thermometer when the latter is carefully used. 29. Leslie's differential Thermometer. Sir John MEASUREMENT BY THERMOMETERS. 23 Leslie has constructed an instrument for shewing the dif- ference in temperature between two neighbouring substances or places, and which is hence called the differential ther- mometer. In this instrument two bulbs, A and B, filled with air are connected together by means of a bent tube, as in Fig. 6 : a little coloured liquid fills the lower part of this tube, and rises to the levels C and D when both bulbs are of the same tem- perature. But should A become warmer than B, since air expands very much for an increase of tem- perature, the column of liquid will be pushed down at C and made to rise at D ; and this motion will be reversed when B becomes warmer than A. Such an instrument will Fi S- 6 - therefore indicate any difference of temperature with great delicacy. The fluid in the tube ought to be one which is not volatile sulphuric acid is frequently used. We shall find afterwards (Art. 165) that the thermo-pile registers any difference of temperature with still greater delicacy than this instrument. 30. Fluctuation Thermometer. The author of this work has proposed an instrument for summing up fluctu- ations of temperature. If a bulb be blown connecting together two horizontal glass tubes of different bores, and if this instrument be nearly filled with mercury, it will be found that this fluid will expand in the tube of wide bore when the temperature rises, and contract in the other when it falls. Thus the mercury will gradually travel toward the extremity of the tube of wide bore, and its position from time to time will indicate the amount of fluctuation which 24 DILATATION OF SOLIDS. the temperature undergoes. This instrument is however difficult of construction. 31. Other instruments for measuring temperature. Wedgwood's pyrometer is an instrument for measuring high temperatures, and its action depends on the contraction which takes place in baked clay when heated. An air thermometer furnishes, however, a much more accurate means of obtaining the same result, and this will be after- wards described. Breguet's metallic thermometer is another instrument which may be used in measuring temperature, but a de- scription of it must be deferred to a future occasion. CHAPTER II. Dilatation of Solids. 32. In the present chapter the relation between the tem- perature and the volume of a solid will be investigated. It is a general, though not a universal law, that when such a body increases in temperature it also expands in volume, or dilates, and that when it diminishes in temperature its volume contracts, so that when restored to its original tem- perature it resumes its original volume. The subjoined apparatus (Fig. 7) is used to illustrate the expansion of solids through heat. A rod A is fixed at one end by a screw J3, while the other end presses against the short arm of a lever, whose long arm P forms a pointer. This pointer exhibits by its movement along a graduated scale any change of length in the rod thus, were the rod to expand, the pointer would be pushed upwards ; and were DILATATION OF SOLIDS. 2$ it to contract, the pointer would fall downwards. Any small change in the length of the rod is thus rendered visible. Fig- 7- But the way in which a solid expands is different ac- cording as the substance is crystalline in its structure or amorphous, and hence the subject naturally divides itself into two parts. In the first of these the expansion of uncrystallized solids will be considered, while in the second the behaviour of crystals under change of temperature will be shortly described. DILATATION OF UNCRYSTALLIZED SOLIDS. 33. In some cases it is the increment of the volume of a body that we wish to estimate, while in others, as for instance when we are considering a substance, such as a bar, of which the length is the important element, it is change of length and not change of volume with which we concern ourselves. The former of these is called linear and the latter cubical dilatation or expansion. We shall commence with linear expansion : but let us first proceed to define what is meant by " the coefficient of expansion," whether linear or cubical. The coefficient of expansion of a sub- stance is the expansion for one degree of temperature of that quantity of the substance whose length or volume (as 26 DILATATION OF SOLIDS. the case may be) was unity at a certain standard temperature, as for instance at the temperature of melting ice. Thus if the length of a brass bar be unity at 32 Fahr., at 33 it will be i.ooooi : hence .0000 1 is the linear coefficient of expansion of brass for i Fahr. 34. Linear dilatation. Lavoisier's method. Several methods of finding the linear dilatation of solids have been proposed. In one of these, namely that adopted by Lavoisier and Laplace, a telescope is placed upon a horizon- tal axis between two pillars, as in Fig. 8. This axis carries a cross piece AB rigidly attached to it, and a bar (not shewn in the figure) fixed at one end is forced to ex- pand by means of heat, and to Fig. 8. press against the cross piece in the direction denoted by the arrow-head. This pressure will move the cross piece and turn round the axis of the telescope to which the cross piece is rigidly attached, so that the telescope will now point to a different object. Suppose that the object to which it is pointing is a vertical scale of inches at a considerable distance. If a horizontal wire be placed in the telescope so as to appear in the centre of its field of view, this will seem to have travelled over a considerable distance on the vertical scale for a very small expansion of the bar. It will be seen that this apparatus is similar to that of Fig. 7, the telescope and vertical scale of inches performing the part of the pointer and graduated quadrant. 35. Ramsden's method. In Roy and Ramsden's appa- DILATATION OF SOLIDS. 27 ratus there are three troughs, the first and the last containing iron bars, while the middle one contains the bar of which Fig. 9. the dilatation is to be measured. To the two extremities of the iron bar contained in the first trough there are fixed the eye-pieces of two microscopes, the object-glasses of which are fixed to the corresponding extremities of the bar in the middle trough. These microscopes are directed towards two marks attached to the extremities of the iron bar in the farther trough. The first and third troughs are kept filled with melting ice, so that the iron bars in these are always of the same temperature. (These bars are per- manently fixed at one end and moveable through a collar at the other.) Hence the points of attachment of the eye- pieces of the two microscopes to the first bar may be regarded as rigidly fixed, as well as the points of attach- ment of the two marks, which are fastened to the extremities of the iron bar in the third trough, inasmuch as there is no expansion or contraction of these two bars through change of temperature. On the other hand, the bar in the middle 28 DILATATION OF SOLIDS. trough is first of all placed in ice, and afterwards in water, of which the temperature is varied by means of lamps, in order that the dilatation of this bar may be measured. This middle trough rests upon rollers, and by means of a screw attached to the table (not shewn in the figure) the left-hand end of the bar is always kept in the same position, so that the object-glass of the left-hand microscope which is attached to the middle bar may be regarded as fixed. But the right- hand extremity of the middle bar, and consequently the object-glass attached to it, is moveable, and will move towards the right when an expansion takes place. At the left side therefore the eye-piece, object-glass, and mark are fixed, while at the right side the eye-piece and mark are fixed but the object-glass is moveable. Now the right-hand eye-piece has in its field of view a vertical thread, which at the beginning of the experiment, when all the three troughs are filled with melting ice, may be supposed to coincide precisely in position with the right-hand mark. But when the object-glass of this microscope has been moved owing to the expansion of the middle bar, this thread will no longer coincide with the mark : nevertheless it may be made to do so by means of a screw attached to the eye-piece and which moves the thread. It is thus apparent that the number of turns and fractional parts of a turn of this screw necessary to bring back the thread to coincidence with the mark affords the means of calculating the expansion of the middle bar, which may thus be determined with very great precision. 36. Pouillet and Daniell's methods. In the last method, as well as in that previously described, the bar of which the dilatation is to be measured is immersed in a liquid, and therefore cannot be heated to a very great extent. If we wish to measure the dilatation of a substance at a high temperature we must use some other method. Pouillet has devised an instrument by which the amount of DILATATION OF SOLIDS. 29 dilatation may be measured at a distant, while Daniell has effected the same object in the following; manner. The bar of which the expansion is to be mea- sured is inserted into A, a black-lead tube, and pushed to the bottom; above it is c il placed an index J?, which is pushed down into contact with the bar, and which is kept somewhat tight by means of a collar CD. When the bar expands through heat this index is pushed up, but is left in its place when the same bar again contracts. Thus by an arrangement similar to that of the maximum thermometer the expansion of the bar may be determined. It may be easily shewn that in this apparatus the index B (neglecting its contraction since it is small) will remain pushed out by a quantity which represents the difference between the expansion of the bar and of the tube containing it. For suppose that at the highest temperature reached the bar and the index B are in contact together. As the temperature falls the bar will contract, leaving a vacant space between the bar and the index; but, on the other hand, the whole tube as it contracts will tend to diminish this vacant space, and to push the bar and the index nearer together. The vacant space will thus be the difference between the expansion of the tube and that of the bar, and indeed it is evident that if the bar be composed of the same material as the tube there will be no vacant space. In using Daniell's instrument it is therefore necessary to obtain independently the expansion of the tube. 37. The following table will exhibit the results obtained by these various instruments, and it is instructive to notice Fig. 10. 30 DILATATION OF SOLIDS. sometimes the coincidence between the determinations of different observers, and sometimes the difference between those of the same observer when operating upon different specimens of the same substance. Table of linear dilatations of solids. Name of substance. Length at 2 1 2 of a rod whose length at 3 2 =1.000000. Name of observer. Glass (tube without lead) (English flint) . . (French with lead) (tube) .... (solid rod) . . . 1.000876 1.000898 1.000918 1.000812 1.000872 1.000776 1.000808 I 000861* Lavoisier and Laplace. Roy and Ramsden. Dulong and Petit 1.001722 Lavoisier and Laplace 1.001712 I 001716 Daniell Brass . ... 1.001867 Lavoisier and Laplace i 001890 (standard scale) (English plate in a rod 5 feet long) (English plate in a trough of 5 feet) Iron, soft (forged) (drawn) . . . wrought . . . 1.001855 1.001893 1.001895 I OOI22O I.OOI235 I.OOII82* I 001156 Roy and Ramsden. Lavoisier and Laplace. Dulong and Petit. Borda Steel (untempered) . . 1 H (tempered yellow) . ,. rod 5 feet . . . Cast iron (prism length 5 feet) . . Lead " . . I.OOI079 I.OOIOSO I.OOI24O I.OOII45 I.OOIIO9 T.OOI072 I 002848 Lavoisier and Laplace. Roy and Ramsden. Daniell. Lavoisier and Laplace. 1.002788 Daniell. Tin (East Indies) . . . (Falmouth) . . . I.OOI938 I.002I73 1.001767 Lavoisier and Laplace. Daniell. * Obtained from the cubical dilatation of these solids (see Art. 41). DILATATION OF SOLIDS. 3 1 Name of substance. Length at 212 of a rod whose length at 32= i.oooooo. Name of observer. Silver (fine) .... (standard of Paris) 1.001910 1.001909 I 001951 Lavoisier and Laplace. Daniell. Gold (de depart) (standard of Paris, not annealed) . ,, (standard of Paris, annealed) . Platinum 1.001466 1.001552 1.001514 1.001230 1.000884* I 0008^7 Lavoisier and Laplace. a M Daniell. Dulong and Petit. Borda. Zinc I.OO2076 Daniell. 38. Remarks on the preceding table. If we suppose that by means of the methods already described a great amount of accuracy of measurement may be obtained, yet there is an uncertainty regarding the real temperature of the experimental bar, and this becomes very great for temperatures above the boiling point of water. In such cases, where a bath is used, it is not only very difficult to keep this at a constant temperature, but it is also very difficult to estimate accurately the temperature by means of a thermometer. This uncertainty with regard to estima- tion applies still more strongly to higher temperatures. But for the range between freezing and boiling water, which is that of the above table, it may perhaps be assumed that the determinations are very good. Whence then pro- ceed the differences between the results of different observers, and even between those of the same observer when estimating the dilatation of different specimens of the same substance ? This is probably due to two causes. In the first place, substances which bear the same name are not always of precisely the same chemical composition. Of these, glass may be mentioned as a prominent example, and accord- ingly we find the dilatation of this substance ranging in the table from .000918 to .000776. Brass, cast iron, and 32 DILATATION OF SOLIDS. steel are likewise compounds of which the composition is variable. But besides this, the commercial varieties of those substances which when pure are elementary, such as iron, lead, silver, gold, &c., often contain a very appreciable amount of impurity, so that the composition of different specimens is by no means uniform. Very often too a comparatively small impurity causes a very great alteration in some of the properties of a metal. In the next place, it ought to be observed that two solids may have precisely the same chemical composition, while yet their molecular condition may be different, owing to a difference in the treatment which they have experienced. Thus steel heated and suddenly cooled is a very different substance from steel which has not been treated in this manner ; and accord- ingly we find that while steel tempered yellow has for its expansion .001240, untempered steel has .001080. Glass also will behave in a different manner according as it is annealed or unannealed, and in certain cases it is almost impossible to obtain two bars, although made of precisely the same material, which shall in all their properties be precisely alike. 39. Cubical dilatation of solids. To determine the cubical dilatation of a solid we may either, first, weigh the substance at different temperatures in a liquid of which the absolute dilatation is known, or we may ; secondly, enclose it in a glass vessel the remainder of which is filled with mercury or water; and if the absolute dilatation of either of these liquids is known, that of the glass envelope and of the enclosed solid may be easily determined. To illustrate this second method let us in the meantime regard the dilatation of mercury as known, and suppose that the following experiment has been made. A glass bottle thoroughly cleansed, so as to admit of being well filled with mercury without air specks, is found to hold DILATATION OF SOLIDS. 33 at 32 Fahr. 10169.3 grains of this fluid, while at 212 it only holds 10011.4 grains. Now it is known from Regnault's experiments (see Art. 52) that the dilatation of mercury between 32 and 212= .018153, tnat is to say, a quantity of this fluid occupying a volume equal to unity at 32 will at 212 occupy a volume - 1.018153. Hence the weight of mercury occupying a given volume at 212 will bear to that occupying the same volume at 32 the proportion of i : 1.018153, and hence (had the bottle not dilated) the weight of mercury filling it at 212 would have been g L - = 9987.9 grains. But the glass envelope having expanded, the bottle holds 10011.4 grains, or 23.5 grains more than it would have held had there been no expansion. The volume of the expanded bottle will therefore bear to that of the same bottle at 32 the ratio of 10011.4 to 9987.9, or of 1.00235 to i ; and hence the expansion of this bottle between 32 and 212 will be .00235. Let us now suppose that this bottle contains a piece of iron weighing 2000 grains, and that the remainder of it is filled with 6707.8 grains of mercury at 32, while at 212 the mercury filling it only weighs 6599.4 grains. There is thus the loss of 108.4 grains of mercury between the two tempera- tures. Had there been no expansion either of the bottle or of the iron the amount of mercury sufficient to fill the bottle at 212 would have been ~ = 6588.2 grains, and 1.010153 there would thus have been the loss of 119.6 grains of this fluid. But we have already seen that the expansion of the bottle enables it to contain 23.5 additional grains of mercury, and hence, had the bottle expanded but not the iron, the loss would only have been 119.6 23.5 = 96.1 grains. The difference between this and the actual loss (108.4 grains) must therefore have been caused by the expansion of the D 34 DILATATION OF SOLIDS. iron, and this must be such that a piece weighing 2000 grains will expand between 32 and 212, so as to occupy an additional volume equal to that occupied by 12.3 grains of mercury at 212. If we assume that the specific gravities of mercury and of iron at 212 are 13.2 and 7.8, we shall find that this additional volume is that occupied by 7.26 grains of iron. Hence of the whole 2000 grains of iron at 212, 7.26 grains are occupying an additional volume, while the re- maining 1992.74 occupy the same volume as that originally 7.26 occupied by the 2000 grains at 32. Hence also 1992.74 = .00364 denotes, according to this experiment, the cubical dilatation of iron between 32 and 212. 40. This example is sufficient to give an idea of the process employed, which may be used for such substances as do not act chemically upon mercury, and even for those metals which do so, provided that they are protected by a thin film of their oxide. The following table exhibits the cubical dilatations ob- tained after this method by different observers; of these MM. Dulong and Petit, and also M. Regnault, employed mercury as their fluid, while, on the other hand, Kopp made use of a flask filled with water. Table of cubical dilatations of solids. Substance. Mean coefficient of expansion for iC between oC and iooC. Mean coefficient of expansion for i c C between oC and 300C. Observer. Glass .00002584 OOOO3O3Q Dulong and Petit ,, (ordinary) .. ,, (crystal; . . Copper . .00002761 .0000228 .00005155 .00003056 .OOOO233 .00005650 Regnault Dulong and Petit 00005 i Kopp Iron Lead .00003546 .000089 .00004405 Dulong and Petit Kopp Tin 000060 Zinc.. . .000080 DILATATION OF SOLIDS. 35 Other substances besides those mentioned in the above table have engaged the attention of observers. M. Brunner (fils) has made experiments on the cubical dilatation of ice. His method consisted in determining the specific gravity of this substance at different temperatures. From these experi- ments he concludes that, while at oC ice has a density of 0.91800, at i9C its density has increased to 0.92013. This would give a cubical dilatation for iC of .000122. 41. Remarks on the above tables. Relation of cu- bical to linear expansion. In comparing this last table with the preceding one of linear expansion we obtain the following result. Comparison of linear and cubical expansions. Mean linear Mean cubical Substance. expansion between 32 Observers. expansion between 32 Observers. and2i2Fahr. and2i2Fahr. f Lavoisier and 1 j" Dulong and Glass ..'.. .000837 < Laplace, Roy V .00254 <^ Petit, [ andRamsden. J - [ Regnault. (" Lavoisier an ~| f Dulong and Copper. . . . .001716 <^ Laplace, \ .005127 S Petit, [ Daniell. j Kopp. (" Lavoisier and ~] Lead .... .002882 < Laplace, \- .0089 Kopp. [ Daniell. (~ Lavoisier and 1 Tin .001959 1 Laplace, Da- \ .0069 ,, [ niell. Zinc.. .. .002076 Daniell. .0080 Iron- .001204 f Lavoisier and "1 < Laplace, I 1 Borda. .003546 )9 {Dulong and Petit. From this it will be seen that the cubical expansion is in every case equal to about three times the linear expansion of the same substance. The reason of this relationship be- tween the two follows at once from the fact that when * an D 2 3 6 DILATATION OF SOLIDS. uncrystallized solid expands it does so in such a manner that its figure at one temperature is similar to that at another. Universal experience demonstrates the truth of this state- ment; and it can be very easily shewn that assuming it to be correct the cubical dilatation of a substance will then be as nearly as possible three times as great as its linear dilatation. For let a represent the coefficient of linear expansion, and a' that of cubical expansion of the same substance for a rise of iFahr. above 32; also letZ and V represent the length and volume of the substance at 32. Then L (i + a) and V (i+a') are its length and volume at 33. But since simi- larity of figure is preserved, we shall have by a well-known proposition in geometry, V\ V(i -fa') : :Z 3 :Z 3 (i + a) 3 ; i : i + a' : : i : (i + a) 3 ; I + a' = (i + a) 3 = I + 3 a + 3 a2 + a 3 - Now since a is a very small fraction we may dispen.se with the last two terms of the right hand member of this equation, and hence i + a = i + 3 a, or a' = 3 a nearly; that is to say, the cubical is equal to three times the linear dilatation. 42. Increase of the coefficient of expansion with the temperature. It will be seen by comparing the mean coefficient of expansion between o and iooC with that between o and 3ooC, that the latter is greater than the former for each of the substances given in the above table ; it would appear, however, that in the case of hardened steel the coefficient of expansion diminishes as the tempera- ture increases ; but this is probably due to the fact that heat deprives the steel of part of its temper, and that it thus becomes more like soft steel, which has a smaller coefficient of expansion than hard steel, as may be seen from the table of linear expansion already given. DILATATION OF SOLIDS. 37 DILATATION OF CRYSTALS. 43. It is found that many crystals do not expand under heat equally in all directions so as to preserve their similarity of figure. Mitscherlich has investigated at great length the action of heat upon crystals, and has obtained the following laws : 1. Crystals of the regular system which do not cause double refraction dilate uniformly in all directions in the same manner as uncrystallized bodies. 2. Crystals that are optically uniaxal are differently affected by heat in the direction of the principal axis and in the direction of the three secondaries, but in the direction of the latter they are similarly affected. 3. Crystals that are optically biaxal dilate unequally in all directions. Mitscherlich believes he has determined, as the result of his investigations, that .the tendency of heat in crystals is to increase the mutual distance of the molecules in that direction in which this is least, so as to equalize the distances in different directions and bring the axes into a state of equality. REMARKS ON THE DILATATION OF SOLIDS. - 44. The general law connected with the dilatation of solids is that enunciated at the commencement of this chapter, which states that such bodies expand when heated, but regain their original volume when they are restored to their original temperature. Neither of these statements is, however, universally true, and a singular exception to the first occurs in the case of Rose's fusible metal. Erman, and afterwards Kopp, have found that there is for this body in the solid state a point of maximum expansion through heat, after which, if the 38 DILATATION OF SOLIDS. temperature be increased, it contracts instead of expanding. According to Kopp something of the same kind takes place in sulphur. 45. In the second place, the statement regarding the re- covery by a solid of its original volume when it resumes its original temperature is by no means absolutely correct. For if a solid be cooled very suddenly, in most cases its particles have not had time to bring themselves into the condition proper to the reduced temperature, and in con- sequence the substance is in a state of constraint, which continues often for a very long time. This is probably the cause of the change of zero in a mercurial thermometer (Art. 22). For when such an instrument is made, or filled, the bulb is heated and suddenly cooled, and hence its parti- cles have not had time to approach so near to one another as they would have done had the process of cooling been very gradual. The bulb is therefore abnormally dilated, and only recovers from this state after a considerable time, during which a slow contraction takes place and the mercury is pushed up in the tube, or the zero appears to rise. In like manner when such an instrument is exposed to the temperature of boiling water and suddenly cooled, the bulb remains somewhat dilated, or the zero appears to have fallen, and only recovers its former position after ten days or a fortnight have elapsed. Magnus, and afterwards Phipson, have noticed a similar behaviour in certain specimens of the idocrase and garnet family. These have their density considerably diminished after they have been heated to a red heat, but in the course of time they recover their former volume. Other instances of this behaviour might be mentioned, and the knowledge of the fact is of much importance in many of the arts. It is accordingly well known to workers in the metals and in glass that the utensils which they form from DILATATION OF LIQUIDS. 39 the molten material require to be very carefully and slowly cooled in order that the particles may have had time to assume their most stable position, otherwise the structure is fragile and comparatively useless. The process by which this is accomplished is called annealing. It thus appears that time is an important element in the cooling of bodies; and with this reservation it may not perhaps be erroneous to assert that a solid body heated and very slowly cooled will regain its original volume on regaining its original temperature. CHAPTER III. Dilatation of Liquids. 46. Apparent dilatation and real dilatation. The cubical dilatation of a liquid may be either apparent or real. By apparent dilatation is meant the apparent increase of volume of a liquid confined in a vessel which expands but in a less degree than the liquid which it contains. By real or absolute dilatation is meant the true change of volume of the liquid without reference to the containing vessel. In order to find the real dilatation of liquids one of the following processes is employed. 47. (I) Method by thermometers. In this method the liquid under experiment is made to fill the bulb of a ther- mometer of which the internal volume or capacity is sup- posed to be known at the various temperatures of observation. This bulb is attached to a graduated stem, and the internal capacity of each division of this stem is likewise supposed to be known. 40 DILATATION OF LIQUIDS. When this instrument has been filled with the liquid under examination it is exposed to different temperatures, and for each of these the position which the extremity of the liquid occupies in the stem is accurately noted. It is clear that by this means the volume of the liquid for each temperature becomes known, and hence the amount of its dilatation may be easily deduced. 48. (II) Method by specific gravity bottle. Here a vessel, the internal volume of which is accurately known for all temperatures, is separately filled at each temperature with the liquid under examination, and the whole is then weighed. The weight of the vessel when empty is also ascertained, and thus the iveight of liquid which it contains at each tempera- ture becomes known. But the volume of this liquid is also known ; hence its density, or the weight of unity of volume, becomes known, and thus the dilatation may be determined. In this method the kind of bottle generally used is one made of glass, having a glass stopper which fits it accurately. This stopper is ground out of a capillary tube, such as that used for the stem of a thermometer, and hence, when the bottle is filled with liquid and the stopper pushed home, any excess of liquid is forced out through the capillary orifice. The bottle ought to be filled in this manner at a temperature lower than that of observation, so that, when it is subjected to the higher temperature and the liquid expands, the excess may escape by the orifice of the stopper and yet leave the bottle quite full. 49. (Ill) Method by weighing a solid in the liquid, or the areometric method. In this method a solid whose volume is accurately known for each temperature of observation is weighed immersed in the liquid at these temperatures. The difference between the weight of this solid in vacuo and its weight in the liquid will give us the means of determining the relative density of the latter at the DILATATION OF LIQUIDS. 41 various temperatures. This will be seen from the following example : Let us suppose that the volume of the solid at 32Fahr. is denoted by unity, but at 2i2Fahr. by 1.006. Suppose also that the apparent loss of weight of the solid when weighed in the liquid at 32 is 1800 grains, while at 212 the same is only 1750 grains: 1800 grains is therefore the weight at 32 of a volume of the liquid equal to unity, while 1750 grains is the weight at 212 of a volume of the liquid equal to i. 006. Hence 1739.56 grains will denote the weight of unity of volume of the liquid at 212; and hence also 1800 grains, which at 32 occupied a volume equal to unity, will at 212 occupy a volume = --- = 1.0347; or the dilata- tion between these two temperatures is represented by .0347. 50. Absolute dilatation of mercury. In all these methods the capacity of the vessel or the volume of the solid employed must be known at the various temperatures of observation, or, in other words, we must know its cubical dilatation. But the remarks in the preceding chapter (Art. 38) lead us to conclude that in order to determine accurately the cubical dilatation of a solid it is hardly sufficient to deter- mine the linear dilatation of another specimen of the same material and to multiply this by three, but the cubical dilatation ought, if possible, to be obtained by direct experi- ment. We have already seen (Art. 39) that in order to accomplish this it is necessary to know the absolute dila- tation of some one fluid, such as water or mercury. The problem before us is thus reduced to the determina- tion of the absolute expansion of some one liquid, after which that of other liquids may be easily derived. This therefore is a determination of much importance ; and since mercury has been chosen for the purpose, we shall now 42 DILATATION OF LIQUIDS. proceed to shew how the absolute expansion of this liqui'd may be found. 51. The method about to be described was first employed by MM. Dulong and Petit. It consists in filling a U-shaped tube with mercury, one limb being kept at a low and the other at a high temperature. The portion of the liquid which is heated will of course be specifically lighter than the other, and hence the hot column must be higher than the cold one, since the two balance each other hydrostatically. Thus if D, D' are the two densities, and ff, H' the corresponding heights, we shall have D : D' : : H' : H, or the heights will vary inversely as the densities. This method is perfect in principle, but it is almost impossible to keep a column of mercury at a constant high temperature and at the same time be able to observe accurately the position of the top of the column. Regnault has however improved the apparatus so as to overcome this obstacle, and the following sketch will give an idea of the arrangement which he employed. ab, a b' are the two vertical tubes to be filled with mercury, and these are connected together near the top by a horizon- tal tube a a. At the bottom they are not connected to- gether, but a b is connected with the horizontal tube b c, and a' b' with b' c' . To the extremities of these horizontal tubes two vertical glass tubes eg, c'g' are attached, and these are both connected with a tube ^'leading to a large reservoir/" supposed to be filled with gas whose temperature is con- stant ; hence the pressure of this gas in the tubes eg, c' g' is also constant. Heat is applied to the tube ab, and by means of an agitator every part of this tube, including the mercury which it contains, may be brought to the same temperature throughout, and the value of this temperature is accurately ascertained. On the other hand, the 'tube a' b' is exposed to a current of cold water of a known constant temperature. DILATATION OF LIQUIDS. 43 The tubes ab, a b' are supposed to be filled with mercury until above the level a a, but we will shew in the sequel that it is not necessary to know the height of the fluid above this level. Fig. ii. Now let / denote the whole pressure due to the left hand column of mercury, and p' the whole pressure due to the right hand column. The pressure at c is evidently />, while that at c is/'. Hence the pressure at d=p pressure of column cd, and in like manner pressure at d' =/' pres- sure of column c' d'. But the pressure at dis equal to that 44 DILATATION OF LIQUIDS. at d', both being equal to the pressure of the gas in the reservoir_/V hence we have p pressure of c d =p' pressure of c' d', and therefore p' p = pressure of column (c' d' c d) . . . (i) that is to say, the difference between the pressures of the two great vertical columns is equal to the pressure of the column of mercury contained between the levels d' and d. Now since the tubes ab, a b' communicate together by a a', it is evident from hydrostatical principles that the portions of the two vertical columns above a a are in equilibrium with each other, and therefore that the pressures of these two portions are equal. But p, or the whole pressure of the" left hand column, = pressure of column a b + pressure of portion above a ; and in like manner/' = pressure of column d b' + pressure of portion above d. Now since the pres- sures above a a are equal, it follows that p' p = pressure of d b' pressure of a b, . . . (2 ) and equating (i) with (2), pressure of (c' d' cd) = pressure of a'b' pressure of a b. We have thus obtained an expression for the difference in pressure between two columns of mercury (ab, a' b'} of equal length but of different temperatures, and since there is no occasion to view the top of the column, we can perfect our arrangements for keeping the whole at the same tem- perature throughout, while by the insertion of an air ther- mometer alongside of a b this temperature may be measured with great exactness. By this means therefore the relative density of mercury at various temperatures may be deter- mined, and its dilatation thence easily deduced. 52. Using this method, and also a modification of it, Regnault obtained results which enabled him to construct a table giving the dilatation of mercury for every ten degrees Centigrade from oC to 350. But before exhibiting this DILATATION OF LIQUIDS. 45 table let us explain the distinction between the mean and the true coefficient of dilatation, as it is quite necessary to know this in the case of liquids which change their rate of ex- pansion from one temperature to another. In general language, if we take a quantity of liquid whose volume at oC is equal to unity, then the true coefficient of dilatation of this liquid at any point is the rate of increase in volume of the liquid at that point, as the temperature goes on regularly increasing. On the other hand, the mean coefficient of dilatation for iC of the liquid between o and any point is the mean rate of increase in volume of the liquid between these two points, that is to say, it is the whole expansion divided by the number of degrees included between the two points. Thus we see in the following table, 2nd column, that the whole dilatation of mercury between o and iooC is .o ! 8153 ; that is to say, a volume of this fluid equal to unity at o will at 100 be equal to 1.018153. Now .018153 is the increase for 100, and hence the mean increase for i will be the hundredth part of this or .00018153, which accordingly will be found in the third column opposite 100, as denoting the mean coefficient of dilatation of mercury between o and that point. On the other hand, the true coefficient of dilatation of mercury at 100 is found by the fourth column to be .00018405; that is to say, if the temperature rises through a very small distance such as i and becomes ioiC there will be an increase of volume represented by .00018405, 46 DILATATION OF LIQUIDS. Table of the absolute dilatation of mercury* True tempe- rature as de- termined by an air ther- mometer (<"). Whole dilatation from o to C of a volume of mer- cury equal to unity at o. Mean coefficient ; True coefficient of dilatation be- j of dilatation tween o and C. I at ZC. | o ... .... .00017905 10 .001792 .00017925 .00017950 20 .003590 .'00017951 .00018001 30 005393 .00017976 .00018051 4 .007201 .00018002 00018102 50 .009013 .00018027 .00018152 60 .010831 .00018052 .00018203 70 .012655 .00018078 .00018253 80 .014482 .00018102 .00018304 9 .016315 .00018128 .00018354 100 .018153 .00018153 .00018405 no .019996 .00018178 .00018455 I2O .021844 .00018203 .00018505 I 3 .023697 .00018228 .00018556 I 4 025555 .00018254 .00018606 I 5 .027419 .00018279 .00018657 1 60 .029287 .00018304 .00018707 170 .031160 .00018329 .00018758 180 .033039 .00018355 .00018808 190 .034922 .00018380 .00018859 200 .036811 .00018405 .00018909 210 .038704 .00018430 .00018959 22O .040603 .00018456 .00019010 230 .042506 .00018481 .00019061 240 .044415 .00018506 .00019111 250 .046329 .00018531 .00019161 260 .048247 .00018557 .00019212 270 .050171 .00018582 .00019262 280 .052100 .00018607 .00019313 2 9 .054034 .00018632 00019363 300 055973 .00018658 .00019413 310 .057917 .00018683 .00019464 320 .059866 00018708 .00019515 330 .061820 .00018733 .00019565 340 .063778 .00018758 .00019616 350 065743 .00018784 .00019666 It will be seen from this table that the true coefficient of dilatation of mercury increases with the temperature. * The accuracy of Regnault's determination of the absolute expansion of mercury has been confirmed by experiments very recently made by Dr. A. Matthiessen by a quite different method. DILATATION OF LIQUIDS. 47 53. Dilatation of water. The determination of the dilatation of water is also a point of much importance; but before proceeding to this subject it will be necessary to notice a very striking peculiarity which this fluid exhibits with reference to its change of volume through heat. If ice-cold water, or water at 32 Fahr., be heated, it does not at first expand as might be supposed, but contracts for about 7 Fahr., and after that begins to expand. It thus exhibits a point of maximum density. This beha- viour was illustrated by Hope by means of the following ingenious apparatus. Fig. 12 represents a glass cylinder filled with water at an ordinary tempe- rature, and having holes made for the insertion of two thermometers, one near the top and the other near the bottom. The middle of the cylinder is surrounded by an envelope filled with a freezing mixture. At first, as the temperature falls, the lower thermometer is very much affected, while the upper one falls but slowly. This con- tinues until a temperature about 39 Fahr. is reached, when the lower thermometer ceases to fall, remaining stationary for some time. On the other hand, the upper one begins to fall more rapidly, and continues doing so until it reaches the freezing point. This behaviour is explained by sup- posing that water attains a point of maximum density at about 39 Fahr., below which it expands instead of con- tracting. At first therefore the particles of water con- tiguous to the freezing mixture becoming denser descend, and are replaced by warmer particles from beneath : and this process goes on until the water below A is reduced to 39 Fahr. ; while, on the other hand, that above the freezing mixture is not so cold. But as the action proceeds, the 48 DILATATION OF LIQUIDS. water contiguous to the freezing mixture having already attained its point of maximum density, becomes specifically lighter instead of heavier, and rising upwards rapidly cools the upper thermometer : all this while the lower thermometer remains stationary at the point which corresponds to the maximum density of water. Many observers have made experiments with the view of determining the temperature corresponding to the maximum density of water, and by the mean of all their determinations this appears to be as nearly as possible equal to 4C, or 3 9. 2 Fahr. Various watery solutions also possess their own points of maximum density ; but a very extensive series of researches made by M. Pierre tends to shew that for other liquids such points do not exist. 54. Having made these remarks on this peculiarity of water and watery solutions, let us now exhibit a table framed by M. Despretz, in which the volume and density of water is given at the various temperatures from 9 to iooC. It may appear anomalous that this table should descend below the freezing point of water, but we shall afterwards see (Art. 98) that this liquid, if kept perfectly still, may be brought to a lower temperature than its usual freezing point without assuming a solid state. These experiments were made according to the method first described in this chapter, or the method by thermo- meters (Art. 47). DILATATION OF LIQUIDS. 49 Table of the density and volume of Water, from gC to iooC, according to M. Despretz (the density and volume at 4 taken as unity). Tempe- rature. Volume. Density. Tempe- rature. Volume. Density. -9 i.ooi 631 i 0.998 371 15 i.ooo 875 I 0.999 125 -8 1.0013734 0.998 628 16 i.ooi 021 5 0.998 979 -7 i.ooi 1354 0.998 865 17 i.ooi 206 7 0.998 794 -6 i.ooo 918 4 0.999 82 18 i.ooi 39 0.998 612 -5 1.000698 7 0.999 302 19 i.ooi 58 0.998422 -4 i.ooo 561 9 o-999 437 20 i.ooi 79 0.998 213 -3 I.OOO 422 2 -999 577 21 1.002 OO 0.998 004 2 i.ooo 307 7 0.999 6 9 2 22 1.002 22 0.997 784 I i.ooo 213 8 0.999 786 23 1.00244 0.997 566 O i.ooo 126 9 0.999 8 73 24 I.OO2 71 0.997297 I i.ooo 073 o 0.999927 25 1.00293 0.997078 2 1.000033 I 0.999 96" 26 I.0032I 0.996 800 3 i.ooo 008 3 o-999 999 27 1.003 45 0.996562 4 I.OOOOOO O I.OOO OOO 28 1.003 74 0.996 274 5 1.000008 2 o-999 999 2 9 1.00403 0.995 9 86 6 i.ooo 030 9 0.999 969 30 1.00433 0.995 688 7 1.000070 8 0-999 9 2 9 40 1.007 73 0.992 329 8 I.OOO I 21 6 0.999 878 50 1.01205 0.988 093 9 i.ooo 1879 0.999 812 60 1.016 98 0.983 303 10 i.ooo 268 4 0-999 73^ 70 1.02255 0.977 947 ii i.ooo 359 8 0.999 640 80 1.02885 0.971 959 12 1.0004724 0.999527 9 1.03566 0.965 567 13 I.OOO 586 2 0.999 4H IOO 1.043 15 0.958 634 I 4 i.ooo 7146 0.999 285 55. Dilatation of other liquids. The dilatations of a great many liquids have been carefully determined by M. I. Pierre, and he has embodied his results in expressions of the following kind 8,= i + at+ bt z + The higher points in this table are subject to considerable uncertainty. 90. Change of density produced in the act of melting. It is probable that most substances expand in the process of melting, so that the liquid is of smaller specific gravity than \;he solid ; but there are some which contract. Ice is a familiar instance of this last class, being considerably lighter, bulk for bulk, than water. According to M. Brunner (fils), (Art. 40), the specific density of ice at oC is only 0.91800, that of water at 4C being reckoned equal to unity. The force with which water expands when it becomes ice is very great. Cast iron, bismuth, and antimony are examples of the same class. On the other hand, mercury, phosphorus, gold, silver, copper, and many other substances, contract as they become solid ; and this is the reason why coins of these three last mentioned metals cannot be cast, but require to be stamped. 91. Latent heat of fusion. When heat is applied to a pound of ice at the temperature of 32 Fahr., it is not instantly G 2 84 CHANGE OF STATE. converted into water, but the process is a very gradual one. The reason of this is that a large amount of heat must first enter into the pound of ice at 32 before it becomes water at 32. This heat is called latent, because it is absorbed by the ice without producing any rise of temperature ; and we may represent the process of liquefaction to ourselves by the following formula : Water at 32 = ice at 32 + latent heat. All substances in passing from the solid to the liquid state absorb heat, and we shall afterwards shew how the amount of this may be measured ; that absorbed by water is very great. The doctrine of latent heat was first taught by Dr. Black of Edinburgh. The great latent heat of water serves to retard the melting of snows. If snow or ice at 32 were suddenly to be converted into water by the smallest addition of heat the inhabitants of valleys would be exposed to terrific inundations, whereas by the gradual melting of ice this is prevented, and by the same means also these inhabitants are furnished with a continuous supply of water. 92. Influence of pressure upon the melting point. Professor James Thomson of Belfast anticipated -theoretically the truth that the melting point of a body which expands in congelation would be lowered by pressure, while that of a body which contracts in congelation would be raised by it. We shall afterwards give the reasoning by which this con- clusion was arrived at; in the meantime we will content ourselves with stating that his brother's idea was verified ex- perimentally by Professor W. Thomson of Glasgow, who shewed that by a pressure of 16.8 atmospheres the freezing point of water (a substance which expands when freezing) was reduced o.232 Fahr. Bunsen afterwards found that the melting points of paraffin and spermaceti, both of which contract when freezing, were raised by the application of pressure. Thus spermaceti LIQUEFACTION AND SOLIDIFICATION. 85 solidified at n7.9 Fahr. under the atmospheric pressure, but under a pressure of 1 56 atmospheres it solidified at 1 2 3.6 Fahr. Hopkins made similar experiments, not only on spermaceti, but also on wax and stearin ; and finally, Mousson, by the enormous pressure of 13000 atmospheres, was able to lower the temperature of freezing water from o to 1 8Cent. 93. Alloys and Fluxes. The fusing point of a mixture of bodies is often considerably lower than that of either of its components : thus, for instance, an alloy of five parts of tin and one of lead fuses at 1 94C. In like manner Rose's fusible metal, consisting of four parts of bismuth, one of lead, and one of tin, fuses at 94C, a temperature lower than that of boiling water. Alloys are much used in soldering and in taking casts. Similar results are. produced by mixing salts together : thus a mixture of the chlorides of potassium and of sodium melts at a lower temperature than either of its constituents. A mixture of equivalent quantities of carbonate of sodium and carbonate of potassium melts below the fusing point of either salt separately, and is used to facilitate the fusion of certain minerals in analysis. In like manner, fluxes are substances which, when added to an ore, promote the formation of a fusible medium. 94. Solution. Substances which change their com- position in passing from the solid to the liquid state. If we have a saturated solution of any salt at the bottom of which are crystals of the same salt, as long as the temperature remains the same there will be no change in the aspect of these crystals ; but in most cases a rise of temperature will cause some of them to dissolve and assume the liquid state.' 95. Freezing mixtures. In solution, just as in fusion, a certain quantity of heat becomes latent ; and this is some- times taken advantage of to produce intense cold. If two solids, or at least one liquid and one solid, on being mixed together produce a compound which is not solid but liquid, 86 CHANGE OF STATE. . we have generally the production of cold. The following table exhibits some of the best known freezing mixtures : Substance, Parts bv weigh,. Sulphate of soda Hydrochloric acid 8 } + 10 to -17. Pounded ice or snow Common salt 1 + 10 to -i 8. Sulphate of soda , t _.o Dilute nitric acid -> j T IO to -19 . Sulphate of soda 61 Nitrate of ammonia 4 + 10 to -26. Dilute nitric acid 4 Phosphate of soda Dilute nitric acid % + 10 to -29. If the substances used and the apparatus have both been previously cooled down, still lower temperatures may be obtained. 96. Influence of pressure upon solution. Mr. Sorby (Proceedings of the Royal Society, vol. xii., April 30, 1863) has found that pressure exercises upon the solubility of salts an influence analogous to that which it exerts upon the melting points of bodies. Thus, when the united volume of the water and of a salt after solution is less than that of the water and salt separately before solution, or, in other words, where solution has diminished the volume, he finds that the effect of pressure is analogous to that which takes place where ordinary fusion diminishes the volume. In this case the solubility is increased by pressure, just as in the corre- sponding case the liability of ice to melt is increased by pressure (see Art. 92). Again, where solution has increased the volume (as, for instance, where sal-ammoniac is dissolved in water), pressure lessens instead of increasing the solubility. PASSAGE FROM THE LIQUID TO THE SOLID STATE, OR SOLIDIFICATION. 97. Substances which do not change their composi- tion in passing from the liquid to the solid state. LIQUEFACTION AND SOLIDIFICATION. 87 We have here two laws of the same nature as those which regulate fusion. 1. Every substance under ordinary circumstances solidifies at a fixed temperature, which is the same as that of fusion. 2. The temperature of the liquid remains at this constant point from the time when solidification commences until it is complete. If a liquid be allowed to cool very slowly, in becoming solid it often assumes the crystalline form, but most frequently we have the vitreous or amorphous state. The crystalline is, however, the most natural condition, and it will always be assumed when the particles have sufficient time to fall into their proper place ; and even after substances have become solid molecular change in the direction of crystallization often takes place. Thus brass or silver if repeatedly heated and cooled becomes brittle, and exhibits a crystalline structure. In like manner, a cannon that has been often fired will at last burst in consequence of a change of this kind ; and the vibrations to which the axles of railway carriages are liable gradually destroy the fibre and toughness of the iron, rendering it crystalline and brittle. 98. It is possible to lower the freezing point by various means. Thus pressure acts in lowering the freezing point of water just as it acted (Art. 92) in lowering the melting point of ice. Again, water deprived of air and allowed to cool very slowly and without agitation may be reduced to 6C while still retaining its fluid state, and if it be enclosed in a tube, its surface covered with a film of oil, and the pressure of the atmosphere withdrawn, it may be reduced to i2C: but under these circumstances the smallest agitation or the presence of a crystal of ice produces solidification. Very frequently a glass vessel filled with water may be found in this state on a cold morning, when the addition of a bit of ice 88 CHANGE OF STATE. in a very few seconds changes entirely the appearance of the liquid. This sudden formation of ice is accompanied by a rise of temperature of the whole liquid, which mounts to the freezing point of water. The reason of this is, that ice requiring much less heat than water, leaves a quantity of heat free to raise the temperature of the whole liquid* A very rapid agitation, or any other cause which, exerting an action upon the molecules, hinders them from assuming the requisite arrangement, retards the formation of ice. Capillary attraction acts in this way ; and M. Despretz has found that in fine capillary tubes water may be lowered to 2OC without solidification. This circumstance probably explains why the sap is not oftener frozen in the capillary vessels of plants. 99. The great amount of the latent heat of water, combined with the fact that ice is lighter than water, are facts of great importance in the economy of nature. To make this clear let us see what occurs when a lake is frozen, supposing that the cold influence or abstraction of heat takes place over the surface of the lake. As the upper layer of water is cooled down it becomes heavier and sinks to the bottom, being replaced by a warmer and lighter layer from below : this process will go on until the whole water of the lake is reduced to 39 Fahr., the point of maximum density of water. When this temperature has been reached the process above described is at an end, and any further cooling of the upper strata will not cause them to sink, since they become specifically lighter below 39. When the surface of the lake has been cooled down to 32 Fahr. it will begin to freeze, but the process of freezing will go on very slowly, since a great quantity of heat must be taken from water before it becomes ice. Again, when a layer of ice is once formed it does not sink LIQUEFACTION AND SOLIDIFICATION. 89 to the bottom, but remains on the top, so that the cooling influence can only freeze a second layer through the substance of the first, and so on. The ice formed thus protects the water below, which remains at 39, a temperature which is not destructive to animal life. 100. Regelation. Faraday was the first to observe a very curious property of ice. Two pieces of thawing ice if put together adhere and become one ; and this adhesion will take place in air or in water, or in vacuo. It would also seem to be independent of the application of pressure; and, provided the surfaces be smooth, when they are brought into the slightest contact, regelation ensues. Nor is it necessary that both surfaces be ice, for wool may be made to adhere to a block of thawing ice after the manner of regelation. The same thing takes place when a snowball is formed. 101. Probably the true explanation of this phenomenon is that advanced by Professor Forbes. He adopts the idea of the gradual liquefaction of ice which was deduced by Person from Regnault's experiments on latent heat, and sup- poses that true hard ice does not pass at once into water, but that there are intermediate stages in the process of liquefaction. The temperature of true hard ice is by this hypothesis essen- tially somewhat less than that of ice-cold water, and the substance corresponding to the intermediate temperature is supposed to appear in a slightly viscous or plastic state, being as yet neither quite solid nor quite liquid, and also to possess probably less than the latent heat of perfectly fluid water. In fact, ice in melting is here supposed to be similar to sealing-wax or wrought iron, both of which substances require a considerable range of temperature in order to pass from the solid to the liquid state, while we may imagine that the whole latent heat is not required until perfect fluidity is reached. The difference between ice and wrought iron in melting would therefore be one of abruptness of transition. 9 o CHANGE OF STATE. Zone, of 31-9 Zone oJ9f-8 317 JZfi In ice the change is accomplished throughout a very small temperature range, in iron it requires a very large one. The subjoined figure will ap- proximately represent the state, as regards temperature, of a cubi- cal block of thawing ice on this hypothesis. 102. Our concep- tion of latent heat (Art. 91) will require to be somewhat mo- Fig. 20. dined in order to suit the hypothesis of gra- dual liquefaction, and we may represent to ourselves what takes place by means of the following diagram (Fig. 21). Let the whole range of tempera- ture between the commencement and the end of the process of liquefaction be denoted by AD, and subdivided into equal parts AB, BC, CD; also let A A denote the whole heat of the body at temperature A; and sup- posing there were no such thing as latent heat, let BB' denote the heat of the body at temperature B, CC' its heat at temperature C, and DD' its heat at temperature D. The latent heat will however have to be added to these heats, in order to ex- press the total heat of the body at the various temperatures. Expressing this latent heat, which is supposed to increase gradually between the two temperatures A and D, by B'B", C'C", D'D", we have the whole lines BB", CC", DD" B' i, \ B C L Fig. 2T. LIQUEFACTION AND SOLIDIFICATION. 91 denoting the whole heat, sensible and latent together, of the substance at the respective temperatures B, C, D. 103. If now it be assumed that hard ice is essentially colder than ice-cold water, we can easily see why two wet pieces of ice will have the water between them frozen when they come into contact. For the ice on both sides of the layer of water will now be colder than it, and hence a new distri- bution of heat will take place, the consequence of which will be that the water will be frozen, becoming as it were the centre of the block. 104. It might be said that the laws of conduction are against this hypothesis, and that we cannot conceive a piece of ice entirely surrounded for a considerable length of time by water at 32, or a little over it, to have in its interior a temperature lower than 32, however small we may imagine this difference to be ; but we think this objection must vanish if it be assumed that the supposed intermediate states between ice and water correspond to intermediate quantities of latent heat. For in this case the heat which is conducted from the outside into the body of a block of ice is not altogether influential in adding temperature, since in each small addition of temperature a certain quantity of heat becomes latent. Let us consider, for instance, what would take place if a large mass of sealing-wax were to be gradually melted by agitation in a pan of liquid sealing-wax over the fire. As the heat was conveyed to the lump of wax, envelope after envelope would become liquid and drop off, mixing with the liquid mass until a very small solid nucleus was left : but as long as there was left a solid nucleus, however small, we should surely be entitled to assume that the temperature of the centre of this nucleus was lower than that of the melted wax. We imagine that there is no impossibility in conceiving that something of the same kind takes place in ice. Heat will no doubt be conveyed into the interior of a block of ice 92 CHANGE OF STATE. that is left for a long time in water a little above 32, but this heat (as remarked by Professor Forbes) will exhibit its action rather in diminishing the size of the block of ice than in completely equalizing its temperature throughout. 105. If we imagine this objection to be obviated by these remarks, there are three questions started by the hypothesis which can only be decided by experiment. 1. Is the interior of a block of ice in fact colder than the exterior ? 2. Is the interior of such a block harder than the exterior? 3. Does soft ice possess more latent heat than hard ice ? With regard to the first of these points certain experiments made by Professor Forbes would seem to indicate that the interior of a block of ice is slightly colder than the ex- terior, For, in the first, place, he found that a thermometer buried in the heart of a block of ice fell decidedly below 32 Fahr., and he also found that rapidly-pounded ice was colder than melting ice. This last experiment has been tried by the author of this work with the same result. With regard to the second point, Professor Forbes has remarked that the surface of a block of ice is much softer than hard cold ice. With respect to the third point, Person's deductions from Regnault's experiments are in favour of the view that soft ice possesses more latent heat than hard ice. Oh the whole, we think the gradual liquefaction of ice is a view which appears not only to be supported by analogy, but to be the best explanation of observed facts: nevertheless it would be desirable that this view should be confirmed by further experiments. 106. Substances which change their composition in passing from the liquid to the solid state. When a solid is dissolved in a liquid until it refuses to dissolve any further, we have what is termed a saturated solution. But what is a saturated solution at one temperature will LIQUEFACTION AND SOLIDIFICATION. 93 not be so at another. In general, a hot liquid dissolves more than a cold liquid. The consequence is that, if the temperature of a saturated solution be diminished, we have a deposition of solid matter in the shape of crystals, and the liquid which is left behind is saturated for the reduced tem- perature. If the solution contain two salts of unequal solu- bility, of different crystalline forms, and having no chemical action upon each other, a greater or less separation of these two salts may be produced by crystallization ; by this means nitre is purified from common salt. 107. Solutions are subject to the same anomalies as water and the like liquids. Thus if we have a solution of Glauber's salt at a high temperature, and if it be allowed to cool gradually and at rest without the admission of air, it will retain the salt in solution, even though the temperature be much reduced. But if it be agitated, or if air be admitted, or, better still, if a crystal of Glauber's salt be dropped into it, crystal- lization will immediately commence, attended, as in the case of water, with a rise of temperature. 108. If instead of a saturated solution we have a weak solution of certain salts, such as sea water, this, when lowered in temperature, will change its state in a different way. At a temperature which is always lower than the freezing point of water such a solution will freeze, producing nearly pure ice and leaving the salt behind. Mr. Walker, who accom- panied Sir L. MClintock in the " Fox," made numerous ex- periments on sea water : he used cold as a means of sepa- rating the salt from the water, but was by this means unable to obtain water of less density than 1.002. Rudorff has made many experiments on this subject, and finds that in saline solutions generally the freezing point is below 32 Fahr., but the extent to which it is lowered de- pends upon the nature of the salt. 94 CHANGE OF STATE. CHAPTER VII. Change of Stale. Production of Vapour and its Condensation. 109. When sufficient heat is applied to a body it generally assumes the gaseous state; unless it be of such a nature that it will under ordinary circumstances be decomposed before assuming this state. By means of a certain applica- tion of electricity, it is probable that the most refractory substances, such as carbon, can be made to appear as gases, although only in very small quantity. Generally when a solid passes into a gas it first assumes the intermediate state of a liquid, but sometimes its passage into a gas is completed without the intermediate form of liquidity being assumed. This is called sublimation; while the passage of a liquid to the gaseous state goes under the general name of vaporization. In whatever way the gaseous condition is produced it always requires a con- siderable amount of latent heat. Thus a pound of water at 212 Fahr. will absorb a great quantity of heat before it is entirely converted into steam, although the steam does not possess a higher temperature than 212. In the same manner as before we may apply the following formula, and say Steam at 212 = water at 2 1 2 4- latent heat of steam. The latent heat of gases is greater than that of liquids, and we will afterwards shew how it may be measured. This latent heat has to be disposed of in some sensible form, when the gas which possesses it is reconverted into a liquid, and thus the latent heat of gases is of great service in retarding the change from the liquid to the gaseous or from the gaseous to the liquid state, which, but PRODUCTION OF VAPOUR AND ITS CONDENSATION. 95 for the great latent heat of gases, would be incon- veniently sudden. Elastic fluids have been divided into gases and vapours, but the distinction between these is merely conventional. A vapour denotes a substance in the gaseous form which at ordinary temperatures appears as a liquid or solid, while a gas denotes a substance which under ordinary circum- stances appears in the gaseous form, and which can only be reduced to the solid or liquid form by intense pressure or intense cold. Our subject may be divided into the following parts. 1 . Vaporization, or the conversion of a liquid into a gas ; and sublimation, or the conversion of a solid into a gas. 2. Liquefaction and solidification of vapours and gases. 3. Elasticity and density of vapours and gases, with a few remarks upon hygrometry. VAPORIZATION AND SUBLIMATION. 110. Vaporization is the general name for a process of which there are three varieties, namely 1. Evaporation, where a liquid is converted into a gas quietly, and without the formation of bubbles. 2. Ebullition, where bubbles of gas are formed in the mass of the liquid itself. 3. Vaporization in the spheroidal condition, where a liquid evaporates slowly, although in apparent contact with a very hot substance. 111. Vapours are formed in vacuo more readily than in air. The presence of air or of any foreign gas retards the formation of vapours, but in vacuo a liquid is very quickly converted into vapour. If a small quantity of water, alcohol, or ether be introduced up through a barometer tube into the Torricellian vacuum at the top, as soon as it reaches this it is converted into vapour, which shews itself 96 CHANGE OF STATE. by lowering the column of mercury by means of its elastic force. This column, which originally denoted the pressure of the atmosphere, now denotes the pressure of the atmo- sphere minus the pressure of the vapour of the liquid. 112. Maximum of pressure in vacuo. If we continue to introduce an additional quantity of the volatile fluid into the Torricellian vacuum of a barometer, we shall at first probably perceive an additional depression ; but as we go on we shall find that the depression does not increase beyond a certain limit, or, in other words, the elastic force of the vapour we have introduced has reached a maximum, and ihe introduction of more liquid will not increase the density of the vapour. We shall further find that the maximum of pressure is regulated by the temperature in such a manner that the higher the temperature the higher is the maximum pressure, so that we are enabled to deduce the following law, first discovered by Dalton : In space destitute of air the vaporization of a liquid goes on only until the vapour has attained a determinate expansive force dependent on the temperature, so that in every space void of air which is saturated ivith vapour determinate vapour pressure corresponds to determinate temperature. The tension of vapour corresponding to a given tempera- ture differs of course with the nature of the substance which is vaporized. Thus the tension of the vapour of water at ordinary temperatures is much greater than that of the vapour of mercury, while the vapours of alcohol and ether have still higher tensions. 113. Mixtures of gas and vapour in a confined space. The experiments of Dalton lead to the following law : In a space filled ivith air the same amount of water evaporates as in a space destitute of air ; and precisely the same relation subsists between the temperature and the expansive force of the vapour, whether the space contains air or not. PRODUCTION OF VAPOUR AND ITS CONDENSATION. 97 Thus if a closed space contain air of. the pressure of 30 inches at a temperature for which the tension of aqueous vapour is 2 inches, and if a little water be introduced, the pressure will rise to 32 inches; while if the same space be void of air the pressure of the aqueous vapour will of course be 2 inches. This law of Dalton has been verified by Gay Lussac. More lately, Regnault has made experiments on this subject, and has investigated the tensions of the vapours of water, ether, bisulphide of carbon, and benzole, both in vacuo and in air. He has found that the tension in air is always slightly less than it is in vacuo, the difference being greater for volatile liquids ; but he is inclined to believe that Dalton' s law is true in principle, and that the differences which he observed are caused by the hygroscopic properties of the sides of the chamber which contained the vapours. 114. Mixed liquids in a confined space. Where a mixture of liquids is allowed to evaporate in a closed space, Gay Lussac inferred that the tension of the mixed vapour was equal to the sum of the tension of the two vapours taken separately. Magnus and Regnault have found that this holds for a mixture of bisulphide of carbon and water, or of benzole and water, of which the components do not dissolve each other ; but in other cases it does not hold. Thus for a mixture of ether and water the tension is scarcely higher than for ether alone. If the liquids mix readily together in all proportions, then the vapour tension is generally less than that of the one liquid and greater than that of the other. 115. Effect of chemical affinity upon evapora- tion. If water be put into a confined space along with some substance which has a great attraction for it and does not readily part with it, the vapour density may be much diminished. Thus if a small quantity of water be mixed H CHANGE OF STATE. with a large quantity of sulphuric acid, the acid will retain the water and will not suffer any of it to evaporate. On the other hand, if we have a large quantity of water and an exceedingly small quantity of acid, we shall have very nearly the usual tension of vapour. Between these two extremes we may prepare solutions of intermediate strength which will diminish to a greater or less extent the tension of aqueous vapour corresponding to the temperature of observation. A similar rule will hold for other solutions ; and if the sub- stance mixed with the liquid whose tension in a state of gas is sought be a fixed and -not a volatile body, its tendency will generally be to prevent the liquid from evaporating, and thus to diminish the tension due to vapour. 116. Tension when two vessels at different tempe- ratures are in communication with each other. In Figure 22, let us first suppose that the stop-cock at C is shut, and that two similar vessels A and B are entirely filled with water and vapour of wa- ter to the exclusion of air or any other gas. Also let A be surrounded with ice, and let heat be applied to B, so that we may suppose A to be at the temperature of melting ice and B to be at 212 Fahr. In this case the tension of the vapour in A will hardly be one-fifth of an inch, while in B it will be 30 inches. Now on opening the stop-cock, there will of course be a rush of vapour from to A, and we may suppose that Fig. 22. PRODUCTION OF VAPOUR AND ITS CONDENSATION. 99 for a moment the pressure of the vapour will be the mean between the two original pressures, but the effect of the cold surface of A will be to condense this vapour and to render it as nearly as possible equal to the tension at 32, viz. one- fifth of an inch. If there be water in B more vapour will rise and pass to A, there to be condensed as before. In fact, the apparatus will now act as a still, and the water of B will be gradually transferred to A. The latent heat, set free by the large quantity of vapour which is condensed at 'A, will of course tend to raise the temperature of A ; but provided this temperature be kept steadily at or near 32 by a sufficiently powerful application of cold, the pressure in A will by this arrangement be kept very low, while the pressure of vapour in B will be somewhat higher than in A, and the dynamical effect of this inequality of pressure in these two vessels will be represented by the rush of vapour from B to A. The intensity of this rush will depend on the intensity of the source of heat : if the heat which enters B be sufficient to produce a large quantity of vapour in a short time, this vapour will rush very fast towards A, and a powerful freezing mixture will have to be applied in order to keep down the temperature of A, but if the source of heat be feeble the rush will be feeble also; in fact, by this arrangement the vapour of water may be regarded as a vehicle for transferring the heat from the source at B to be spent in liquefying the ice or freezing mixture, or to be otherwise disposed of at A. If in the first part of this experiment, when the cock C is shut, the vessel B contains no water in a liquid form, but is entirely filled with the vapour of water at 212, then when C is opened this vapour will be almost immediately con- densed at A, and an approximate vacuum will be formed. We shall afterwards see how this principle has been applied by Watt in the steam-engine. H 2 IOO CHANGE OF STATE. It will be evident that the perfection of vapour as a vehicle for carrying heat, as described above, depends upon the absence of air in the arrangement of the experiment. For if A and B be filled with air, each particle of vapour which is carried from B to A must pass through all this air, and the transmission of vapour will in this case be very difficult. There are various useful applications of the process de- scribed above. The first we shall mention is 117. Distillation. The subjoined figure will represent this process. The liquid to be distilled away is contained in A. It generally exists combined either with some fixed im- purities or with some other liquid less volatile than itself, and the object of distillation is to separate it from these. This is done by applying heat to A and by attaching to it a Fig- tube, as in Fig. 23, the other extremity of which passes in coils through a vessel of cold water. The liquid is vaporised by the applied heat, and is then driven through this tube, but as it passes through the coils immersed in the cold water (technically called the worm), a comparatively large surface is exposed to the cooling agent, and the vapour is rapidly PRODUCTION OF VAPOUR ANDJTS C\OjVB'*f34 PIO&. /JO I condensed, passing in drops from B into a bottle prepared to receive it. The vessel C through which the worm of the still passes must be kept cool : this is done by constantly supplying it at a low level with cold water by means of a tube at D, and by withdrawing the hotter and therefore lighter layers of the water at C ; a constant current of cold water is thus made to circulate through the vessel. 118. Cold due to evaporation. Freezing apparatus. Whenever vapour is produced a quantity of heat is rendered latent. This heat is necessary to the formation of vapour, and must be supplied either from some foreign source, or, if this be not available, from the very liquid which is being evaporated. In this last case the temperature of the liquid falls in order to supply the heat necessary to the existence of vapour. Leslie was the first to freeze water by means of the drain of heat caused by its own evaporation. In his experiment a vessel containing strong sulphuric acid is placed under the receiver of an air-pump, and above it a thin metallic vessel containing a little water. As the receiver becomes exhausted the water evaporates more and more rapidly, and the vapour, as fast as it is formed, is ab- sorbed by the sulphuric acid. The vapour thus becomes a vehicle for carrying heat from the metallic vessel, and the con- sequence is a diminution in temperature until ice is formed. An instrument called the cryophorus, or frost carrier (Kpvos frost, (J>opbs bearing), very similar to that of Fig. 22, is some- times used to shew the freezing of water from its own evaporation. Thus if we. suppose all the water to be in B, and only vapour of water without air in A , and if A is cooled by a powerful freezing mixture, while B is not exposed to a source of heat, then rapid evaporation of the water in B will take place, and this vapour will go to A and be condensed there as fast as it is formed. T02 'CKANGF- 0>. STATE. Heat is thus carried, as before, from B to A, but as there is now no source of heat at B the water there must part with its own heat in order to furnish that which is necessary for evaporation, in consequence of which it will be frozen. In this experiment it is well to protect B from the influence of currents of air. When other liquids and mixtures more volatile than water are used in this manner, a very intense cold may be produced. Thus by the evaporation of liquid sulphurous acid a degree of cold is obtained sufficiently strong to freeze mercury. By a mixture of solid carbonic acid and ether Faraday obtained a degree of cold which he estimated at 166 Fahr. ; and more recently, Natterer, by mixing liquid nitrous oxide with bisulphide of carbon, and placing them both in vacuo, has obtained 2 20 Fahr. In hot climates porous vessels called alcarazas are used for cooling water. The water reaches the outside through the pores, and hence a continual evaporation is going on, especially when the vessels are placed in a current of air. MM. Carre and Co. of Paris have invented a very ingenious freezing machine, which was ex- hibited in London at the International Exhibition of 1862. This apparatus is re- presented in Figs. 24 and 25. A is a strong vessel of wrought iron three- quarters filled with a concentrated solution of ammonia. B is a strong wrought iron circular condenser having a central space sufficiently large to receive the vessel PRODUCTION OF VAPOUR AND ITS CONDENSATION. 103 D. The pipes are so arranged as to prevent the liquid from boiling over into the condenser. Before using the in- strument it is laid upon its side, boiler downwards, for about 10 minutes, so as to allow any liquid that may be in the con- denser to drain back into the boiler, and this is facilitated by heating the condenser slightly with a lamp. Fig. 25. The process consists of two parts. In the first of these, Fig. 25, the boiler is heated very gradually by a charcoal chauffer, or other source of heat, while the condenser B is kept in a vessel through which a stream of cold water is constantly flowing. As the result of this pro- cess, the ammoniacal gas separates from the water and is condensed by its own pressure in B, and the heating is allowed to go on until a thermometer attached to the boiler indicates about 270 Fahr., at which temperature it is pre- sumed that nearly all the ammoniacal gas is condensed in B, while all the water remains behind in A : the second part of the process next begins. The apparatus is now withdrawn from the fire ; the water is allowed to run out of the orifice B through a hole in the bottom; this orifice is then stopped with a cork, and the cylinder D containing the liquid to be frozen is put into JB, a little alcohol having been previously introduced in order to establish a liquid communication between the sides of B and Z); the vessel A (Fig. 24) is now plunged into water which is kept cool, while the condenser is wrapped round with flannel J04 CHANGE OF STATE. a non-conductor. The temperature of A now falls very rapidly, and as the water in A reacquires its power of absorbing ammoniacal gas, this gas rises very abundantly from , and is condensed in A. In consequence of this rapid evaporation B becomes intensely cold, and if it contains water this will be frozen. Mercury may also be frozen by this means. As the success of this instrument depends upon its being devoid of air, there is an arrangement of the following kind, by which any air can be got rid of. G is a small cup which is always kept full of water, and in it works a screw, so that when relaxed it opens up an exceedingly small entrance into the interior. When the temperature of the boiler has risen to about 1 40 Fahr. the screw is slightly loosened, and the disen- gaged ammoniacal gas is rapidly absorbed by the water in G. If any air be present, this will be seen by its rising to the surface, and the channel must be kept open so long as such an appearance of air continues, but when the gas is wholly dissolved by the water, the screw must be again tightened and the operation of heating continued. A portion of the boiler at Z>, Fig. 25, is made of metal which will fuse below that temperature at which the pressure of the steam would burst the boiler. This arrangement acts therefore as a safety-valve. 119. Tension in communicating vessels filled with air. Dalton, as we have already mentioned, was the first to shew that in a space filled with air the same amount of water evaporates as in a space destitute of air; and that precisely the same relation subsists between the temperature and the maximum vapour tension whether the space con- tains air or not. Unfortunately there has been based upon this experimental result a theory which is only a possible but not a necessary result of these experiments. It has been sup- posed that no mutual relation whatever exists between vapour PRODUCTION OF VAPOUR AND ITS CONDENSATION. 105 and air, and that they remain near each other without pro- ducing the slightest mechanical effect upon one another. This theory has come to be too much regarded as a neces- sary result of Dalton's experiments, although certain observa- tions made by Bessel, Broun, Welsh, and others seemed to be incapable of explanation by it. Dr. Lament of Munich has devised a crucial experiment, the result of which has been to refute this hypothesis. The arrangement adopted was of the following nature. A glass tube, bent as in Fig. 26, had at one end a globe K, while the other end e is left open to the atmosphere, q is a drop of quicksilver, which is Fig. 26. capable of moving backwards and forwards along de. The curved part ckd of the tube is plunged into a vessel BB filled with cold water, while into the vessel A A, in which the globe K is placed, cold and warm water can alternately be poured. The experiment was of the following nature : sup- pose that before commencing it the temperature of the whole apparatus as well as of the water in BB is 32 Fahr., and suppose also that the globe and tube are filled with dry air of the pressure of 30 inches. First raise the temperature of the globe K to 1 00 Fahr. by pouring warm water into A A, while the temperature of bcde remains as before. Owing to the increased elasticity of IO6 CHANGE OF STATE. the dry air, the quicksilver q is pushed toward e\ notice how far. Next cool down the globe to its former temperature (32), and introduce a little water into K by breaking off the fine point a, which is then sealed on again, and repeat the previous experiment that is to say, heat the globe to 100 Fahr. as before, and again notice how far the quicksilver is pushed towards e. The result of this experiment will be a test of the truth of this hypothesis. . Let us see, in the first place, what ought to take place if these views are correct; that is to say, if the vapour and air are quite independent of each other. For simplicity's sake we may imagine the second heating of the globe to take place not a very long time after the intro- duction of the water, in which case the vapour will not yet have penetrated to q (in Lament's experiment there was no trace of vapour at this part of the apparatus). If these views be correct, there being no tension of vapour at q, the pressure there will be entirely due to dry air. No doubt there is pressure of vapour in the globe K, but by this hypothesis it has no effect on the particles of dry air, and cannot therefore be communicated to q. The drop of quicksilver at q ought therefore to move, for a given heating of the ball, precisely the same distance whether the air of the globe be dry or whether it contain vapour. Let us now suppose, instead of this hypothesis, that the air exerts a pressure upon the vapour and the vapour upon the air. Then the globe K will have a tension of vapour corresponding to 1 00 Fahr. = 1.9 inches nearly; this has to be added to the tension of dry air, and the sum will be communicated through the dry air of the tube to the quick- silver at g, which will, on this hypothesis, be pushed much further when there is vapour than when there is only dry air. On the other hypothesis, however, as we have seen, the quick- PRODUCTION OF VAPOUR AND ITS CONDENSATION. 1 07 silver will be pushed equally far in both cases. Now Lament found that the quicksilver was pushed much farther when there were air and vapour together than when there was only dry air, and he therefore concluded that the first hypothesis is incorrect. 120. Various modes of vaporisation. Our attention has hitherto been directed to certain laws which have no special reference to the particular modes in which vaporisation is accomplished. Let us now consider the peculiarities of these various modes. We have already (Art. no) stated that there are three such viz. evaporation, ebullition, and vaporisation in the spheroidal state. Let us begin with the first of these. 121. Evaporation. Evaporation denotes the quiet pro- duction of vapour at the surface of a liquid, and is subject to the following laws. 1. It varies with the temperature. 2. It varies with the extent of surface exposed. 3. It goes on very rapidly in vacuo, but much more slowly in a space filled with air. 4. It goes on more rapidly in dry air than in air con- taining vapour. 5. It is assisted by any agitation tending to renew the particles of air over the evaporating surface. The reason of the fourth and fifth laws is very evident. When vapour forms above the surface of a liquid in still air, it rises so slowly that the air above the liquid soon becomes saturated with vapour, or nearly so, and hence the evaporation, if not quite stopped, yet proceeds very slowly. But when new and comparatively dry particles of air are constantly brought into contact with the liquid the process is greatly facilitated. This process is constantly going on in nature, and forms one of the means by which the surface of the earth is 108 CHANGE OF STATE. rendered fit for the maintenance of living beings ; it is also of very extensive application in chemistry and in the arts, being employed to separate a volatile from a fixed substance. 122. Ebullition. When a liquid is heated in an open vessel it gradually gets hotter and hotter, and the evaporation more and more rapid. After some time the layers of liquid in contact with the sides of the vessel become changed into vapour, which begins to rise, but is condensed by the colder strata before it reaches the surface. This is the cause of the singing noise of liquids before they begin to boil. Soon, however, the bubbles of vapour are able to reach the surface, and the process of ebullition has begun. The temperature now ceases to rise, and remains stationary until the whole of the liquid has been boiled away. The temperature of ebullition depends, (i) on the external pressure ; (2) on the nature of the vessel ; (3) on the sub- stance dissolved in the liquid ; (4) on the nature of the liquid. 123. Influence of pressure upon the boiling point. It may be easily shewn, by an arrangement like that of Figures i and 2, that the elastic force of vapour during ebullition is equal to the external pressure, for it will be found that the level of the liquid is the same on both sides of the gauge. We see now what takes place when a liquid is heated in the open air. Its temperature will continue to rise until that point for which the corresponding vapour tension is equal to the external atmospheric pressure. The temperature of the boiling point will thus be low when the pressure of the air is low, and high when this is high. The following experiments will illustrate the effect of pressure. First experiment. -Let a flask half filled with water be boiled until all the air has been driven out of the upper part of it, which is filled with steam instead. If it now be corked tightly and inverted, it will very soon cease boiling ; but if cold water be poured upon it ebullition will commence PRODUCTION OF VAPOUR AND ITS CONDENSATION. 109 anew : the reason being that the cold water by condensing the vapour with which the upper part of the flask is filled withdraws the pressure from the water, which is thus enabled to boil at a comparatively low temperature. Second experiment. Put a vessel containing ether under the receiver of an air-pump. Exhaust the receiver, and the ether will begin to boil at the ordinary temperature. It follows from these experiments that at the top of a lofty mountain, where the pressure of the atmosphere is much diminished, the temperature of the boiling point of water will be much reduced. At the top of Mont Blanc, for example, water boils at about 185 Fahr. The temperature of boiling water at high elevations is often too low for culinary purposes, and those who live in such places are therefore com- pelled to heat water in a closed vessel under a pressure greater than that of the atmosphere in order to prepare their food. This is done by means of an apparatus invented by Papin, a French physician, and which bears the name of Papin's Digester. It consists simply of a strong closed vessel to contain the water to which heat is applied. When the pressure rises too high the vapour escapes by means of a safety-valve. There is thus a limit depending on the strength of the vessel, beyond which the pressure and temperature cannot mount, but this limit is sufficiently high to permit of the contained water doing great service in culinary operations. This appa- ratus is often used at the level of the sea, since water is much more efficient in extracting gelatine from bones at a high temperature than at the ordinary boiling point. Boiling-point thermometers are sometimes used for in- dicating, by means of the temperature of ebullition, the pressure of the air, and thus determining the heights of moun- tains. Such instruments perform the part of a barometer, while they are more portable. Their scale embraces a temperature range generally extending only from about 30 below 212 to 110 CHANGE OF STATE. a few degrees above this point ; it is thus very open, and the temperature of the boiling point may be very accurately observed. Mountain thermometers are accompanied by an apparatus similar to that of Fig. i, devised by Regnault, and fitted in this case with telescopic joints, in order to make it easily portable. 124. Influence of the nature of the vessel upon the boiling point. Gay Lussac was the first to observe that water has a higher boiling point in a glass vessel than in a metal one. He attributed this to the adherence of the molecules of water to the glass. M. Marcet and others have since made many experiments on this subject. It is found as the result of these that the boiling point of water in a glass vessel under the pressure of 760 millimetres may be raised as high as io2C. If the interior of the vessel be varnished with shell-lac the temperature may even rise to io5C before the water begins to boil : ebullition will then take place in bursts, each burst causing the temperature to fall. If, however, iron filings be dropped into the glass vessel, the temperature of the boiling point is lowered ; and if the vessel itself instead of being glass be made of metal, the temperature is reduced nearly to iooC. On the other hand, the temperature of the vapour arising from the water is as nearly as possible the same in all these cases. Hence we see that while the temperature of the vapour remains constant, that of the liquid varies according to the nature of the vessel; we ought also to state that in all cases the temperature of the vapour of water is below that of boiling water. 125. Influence of substances dissolved upon the boiling point. Magnus, Marcet, and others have made experiments on saline solutions of different kinds and strengths, from which it appears that the general effect of the salt is to raise the temperature of ebullition. In this PRODUCTION OF VAPOUR AND ITS CONDENSATION. Ill case also (just as in the case of pure water), the temperature is highest in glass vessels and lowest in metallic ones. Ac- cording to these experiments the salt has the effect of raising the temperature of the vapour as well as that of the liquid. Regnault, who has investigated this subject, concludes that the vapour is at first in temperature equilibrium with the boil- ing solution, but that it is quickly cooled, so that the results obtained by Rudberg, who found that the vapour of a solution possesses the same temperature as if it were disengaged from pure water at the same pressure, may be considered correct. In practice the temperature of the vapour of moderately pure water in an apparatus similar to that of Fig. i may be con- sidered to be regulated entirely by the atmospheric pressure. 126. Influence of air dissolved upon the boiling point. Magnus had made the observation that if water could be boiled in a vessel formed as it were of water itself, or in a vessel the sides of which would retain the water everywhere with the same force as that which its particles exert upon each other, we should then know the true boiling point of water, and he calculated that under such circumstances water would not boil until about io5C, so that the dif- ference between the elastic force of vapour at this tempe- rature and that due to 100, or about one-fifth of an atmosphere, is the measure of the cohesive force of the particles of water. M. Donny was afterwards led to conclude that the boiling point of perfectly pure water is considerably above that determined by Magnus, and that the cohesion of the particles is very great. By depriving the water of air as far as possible by long continued boiling and by enclosing it in a peculiarly shaped vessel, he was able to raise its temperature to i35C without ebullition, and even higher temperatures have since been obtained. Mr. Grove has recently made experiments on this subject, and has found that even after water has been long 112 CHANGE OF STATE. boiled it is not quite deprived of all traces of nitrogen ; and he has gone the length of saying that no one yet has seen the phenomenon of pure water boiling, that is, of the dis- ruption of the liquid particles of the oxy-hydrogen compound, so as to produce vapour, which will condense into water, leaving behind no permanent gas. 127. Influence of the nature of the liquid upon the boiling point. Some liquids, such as ether and sulphurous acid, have very low boiling points, while others, such as mercury, have very high ones. The following table of boiling points and specific gravities has been constructed by Dr. W. A. Miller, and is derived chiefly from the labours of Pierre and Kopp. Table of boiling points and specific gravities of liquids. Name of Substance. Boiling point, Fahr. Specific gravity at 32 Fahr. Observer. Sulphurous anhydride .... Chloride of ethyle I 7 .6 ci.q 0.9214 Pierre Bromide of methyle cc.c 1.6644 Aldehyde 60 A. O.SoOQ Kopp Formiate of methyle . . . 02. 1 0.0084 Ether y-i.i QA 8 yj t 0.7365 Bromide of ethyle Iodide of methyle Bisulphide of carbon . . . . Formic ether 105.8 III-4 II8.5 127 7 M733 2.1992 1.2931 O.Q357 Pierre Acetone 132 -3 0.8144 Kopp Acetate of methyle Chloride of silicon 133-3 T?8 2 TT 0.9562 1. 5237 Pierre TjC A 3.1872 I4Q Q o.8i7o Kopp Iodide of ethyle itf 5 1.07^^ Pierre 8 IOJ Q o oc6o Alcohol Terchloride of phosphorus . I73-I 173-4 176.8 0.8151 1.6162 0.8001 )) Kopp Dutch liquid 184.7 1.2803 Pierre Butyrate of methyle Water 2 204.6 212. 0.9209 1 .0000 Kopp 221 K, 2^8.8 0.0041 " 24.O.2 2.2671 Pierre PRODUCTION OF VAPOUR AND ITS CONDENSATION. 113 Name of Substance. Boiling point, Fahr. Specific gravity at 32 Fahr. Observer. Valerate of methyle 24.1.1 o oom Kopp Acetic acid Fousel oil 243-1 260 8 o 8271 i) Pierre Bromide of ethylene 270.0 Terchloride of arsenic . . . Perchloride of titanium.. . . Bromide of silicon 273.0 276.6 qoS o 2.2050 1.7609 2 8l28 Butyric acid 3i 219.90 1264.83 857.07 535-05 55 278.59 1481.06 1001.57 637-7I 60 35 21 1725.01 1164.51 755-44 65 436.90 1998.87 I347-52 889.72 70 541 - T 5 2304.90 1552.09 1042.11 75 665.54 2645.41 1779.88 1214.20 So 812.91 3022.79 2032.53 1407.64 85 986.40 3439-53 2311.70 1624.10 90 1189.30 3898.26 2619.08 1865.22 95 1425.13 4401.81 2966.34 2132.85 100 1697-55 4953-30 3325. J 5 2428.54 105 2010.38 5556-23 Z1*1> 1 9 2754-03 no 2367.64 6214.63 4164.06 3110.99 115 2773.40 6933-26 46374 1 3501.03 120 323I-73 7719.20 5 J 4 8 -79 392574 145. The change of condition from liquid to solid is without influence on vapour tension. From experi- ments made by Gay Lussac and Regnault it would appear that the passage of a substance from the liquid to the solid state is ivithout influence upon the vapour densities, so that in the curve which embodies M. Regnault's observations on the elasticity of aqueous vapour there is no break at the freezing point. PRODUCTION OF VAPOUR AND ITS CONDENSATION. 133 146. Dalton's hypothesis regarding vapour ten- sions. Dalton supposed that the tensions of all vapours would be equal at equal distances from their respective boiling points. Thus, for example, water boils at 2i2Fahr. and alcohol at 173. Of course at these temperatures the tension of both vapours is equal, being represented by one atmosphere, or 30 inches of mercury. According to Dalton the tensions of these two vapours will also be equal at 212 10 = 202 and 173 10 = 163. This hypothesis of Dalton does not generally hold, but for short distances on either side of the boiling point it holds approximately in a large number of instances. 147. Density of gases and vapours. When sub- stances are compared together in the state of gas at the same temperature and pressure, a very simple relation is found to subsist between their density and their combining chemical equivalent. This was first discovered by Gay Lussac, who found that when gas or vapours combine together, the volumes in which they combine bear a very simple ratio to one another. The following table, kindly furnished by Dr. Williamson, will serve to illustrate this law, which is gene- rally called the law of volumes. The new notation is used. ,.. r Vapour volume of elements libe- Vapour volume of compounds. rated from Hydrochloric acid (H Cl) 2 vols. ... I vol. hydrogen + I vol. chlorine. Hydrobromic acid (H Br) 2 vols. ... I vol. hydrogen +l vol. bromine. Hjdriodic acid (HI) 2 vols. ... I vol. hydrogen 4-1 vol. iodine. Steam (H 2 O)2 vols. .. 2 vols. hydrogen +l vol. oxygen. Ammonia (NH 3 )2vols. ... I vol. nitrogen + 3 vols. hydrogen. We see from this table that equal volumes of chlorine and hydrogen, for instance, combine together without change of volume to form hydrochloric acid gas, which contains one atom of hydrogen united to one of chlorine. Equal volumes of chlorine and hydrogen contain therefore an equal number of atoms of these elements. 134 CHANGE OF STATE. There are thus three laws which bear immediately upon the density of gases, i . The above law of volumes, in which the density of a gas at a given temperature and pressure is shewn to depend upon its chemical constitution; 2. Boyle's law, in which the density of a gas of a given constitution and temperature is shewn to depend upon its pressure; 3. Gay Lussac's law, in which the density of a gas of a given constitution and at a given pressure is shewn to depend upon its temperature. 148. Many experiments have been made with a view to determining whether these three laws hold for all gases and vapours, and we shall now very briefly indicate the various methods pursued in these investigations. In the first place, Gay Lussac's method in his researches consisted in ascertaining the volume occupied by a known weight of liquid when entirely converted into vapour at a certain temperature and pressure. It is, however, essential to this method that the whole of the liquid should be converted into vapour, and hence it is inapplicable to a gas at its maximum density and in contact with its own liquid. It only applies to these cases when the density is considerably inferior to that of saturation. No doubt the density of saturation might be calculated from an experiment of this kind, if we supposed Boyle's law to hold good; but one great object of such experiments is to determine whether this law holds accurately for gases near their point of saturation. In order to obviate this objection M. Despretz introduced a method which consists in filling with gas or vapour at different temperatures and pressures a balloon of known weight screwed on the top of a barometer tube. Afterwards Dumas, in order to experiment upon gases that act upon mercury, and to obtain results at high tem- peratures, used a glass balloon, which he arranged so as to PRODUCTION OF VAPOUR AND ITS CONDENSATION. 135 be filled with the vapour of a liquid at a temperature 20 or 30 above the boiling point of the liquid, and under the ordinary atmospheric pressure. More lately Regnault has made several series of experi- ments on this subject. 1. His first series was on the density of aqueous vapour in vacuo at the temperature of boiling water, and under a pressure not exceeding half an atmosphere, and he found that both Boyle's and 'Gay Lussac's laws were applicable within the limits of his experiments, but when the pressure approached more nearly to its maximum, he found that the density increased more rapidly than the elastic force. 2. His second series was on the density of aqueous vapour in vacuo at temperatures not very far removed from that of the surrounding medium, and from these he concludes that the density of aqueous vapours in vacuo and under feeble pressures may be calculated according to Boyle's law, provided that the fraction of saturation does not exceed 0.8, but that this density is notably greater when we approach more nearly to the state of saturation. He adds, however, that this latter circumstance may be owing to one or both of two causes ; either aqueous vapour really suffers an anomalous condensation on approaching its point of satu- ration, or a portion of the vapour remains condensed on the surface of the glass, and does not assume the aeriform state until the mass of vapour is at some distance from the point of saturation. 3. Regnault has also examined the density of aqueous vapour in air at its maximum value for the temperature of experiment between the limits o and 25C, and he concludes that the density of aqueous vapour in air, in a state of satu- ration and under feeble pressures, may be calculated, without much error, from Boyle's law. Messrs. Fairbairn and Tate have lately made experi- 136 CHANGE OF STATE. ments to determine the density of steam at different tem- peratures, and to find the law of expansion of superheated steam. The general plan of their method of ascertaining the density of steam consists in vaporizing a known weight of water in a large glass globe with a stem, of known capacity and devoid of air, and observing the exact temperature at which the whole of the water is just vaporized. In the following table the authors exhibit the relation between the specific volume, pressure, and temperature of saturated steam as determined from their experiments. Specific volume denotes the number of times the volume of steam exceeds the volume at 39.! Fahr. of the water from which it is raised. Pressure in inches of mercury. Maximum temperature of saturation, in degrees Fahr. Specific volume of steam. 5-35 136.77 8275-3 8 62 155-33 5333-5 9-45 I59'36 4920.2 12.47 17092 3722.6 12.61 171.48 37I5.I 13.62 174.92 3438.1 16.01 182.30 3051.0 18.36 188.30 2623.4 22.88 198.78 2149-5 53-61 242.90 943-1 55-52 24482 908.0 55.89 245.22 892.5 66.84 2 55.5o 759-4 76.20 263.14 649.2 8153 267.21 635-3 84.20 269.20 605,7 92.23 274.76 5844 90.08 2 7330 543-2 99.60 279.42 5i5-o 104.54 . 282.58 497.2 112.78 287.25 458.3 122.25 292.53 433-1 114.25 288.25 449-6 PRODUCTION OF VAPOUR AND ITS CONDENSATION. 137 With regard, in the next place, to superheated steam, the results of these experiments shew that for temperatures within about ten degrees from the maximum temperature of satu- ration, the rate of expansion on account of heat greatly exceeds that of air, whereas at higher temperatures from this point the rate of expansion approaches that of air, so that as the steam becomes more and more superheated, the coefficient of expansion approaches that of a perfect gas, while at or near the maximum temperature of saturation the coefficient of expansion greatly exceeds that of a per- fect gas. We thus perceive that near their points of saturation gases and vapours would appear to depart both from Boyle's and from Gay Lussac's law, while probably if the pressure under which they exist be far inferior to that of saturation these laws are obeyed. Generally speaking we may presume that the three laws to which we have before alluded as regulating gaseous density (namely the law of volumes, Boyle s law, and Gay Lussac's law), only hold accurately in the case of perfect gases. 149. Regnault has furnished us with the following deter- mination of the weight of a litre of the most important gases. Weight of one litre (61.02705 cubic inches) of air, oxygen, hydrogen, nitrogen, and carbonic acid gas. Name of gas. Density. Weight at o c C and under the pressure of 760 millimetres of mercury reduced to oC at the latitude of Paris. ( = 29.914 inches of mercury at 32 at London.) Air I 20^187 grammes Oxygen Hydrogen Nitrogen Carbonic acid . . 1.1057 0.0693 0.9714 1.5291 1.429802 0.089578 1.256167 I-9774H 138 CHANGE OF STATE. We have also the following densities of vapours. Air I i.oooo Vapour of water .... I 0.6235 alcohol .. | 1.6133 ether .... | 2.5860 Gay Lussac and Thenard. Gay Lussac. Gay Lussac. 150. Hygrometry. Hygrometry is that branch of science which treats of the state of the air with regard to moisture. As this is one of the elements which form the climate of a place, and as the human body is very much affected by the hygrometric state of the air, the subject is one of much practical importance. There are several facts regarding the vapour present in the air which it is very desirable to know. 151. One of these is its Tension. Suppose that we were to isolate in a vessel a cubic foot of air, allowing it to re- main at its present temperature and pressure, and then to introduce into the vessel containing it a substance which absorbs moisture ; the air by this means will be rendered dry, and its tension will be diminished by an amount representing the tension of aqueous vapour present in the air. It is of importance to know what this tension is, for upon this, among other things, depends the behaviour of the air when it is cooled down. If, for instance, at the higher tem- perature there be present nearly as much aqueous vapour as the air can contain at that temperature, then if the air be cooled down only a few degrees, some of this vapour will be deposited in the liquid or solid state. The temperature at which this takes place is called the dav-point. We thus see that if the tension of vapour in the air at its existing tem- perature be great the dew-point will be high, but if this tension be small, the dew-point will be low in the thermo- metric scale. 152. Another object of research is the relative humidity PRODUCTION OF VAPOUR AND ITS CONDENSATION. 139 of the air. Of course all substances exposed to the air will be affected by the deposition of moisture when the dew-point is reached, but many substances will be affected long before this takes place ; our bodies, for instance, will experience the wetness of the air long before. On the other hand, if the present temperature be far above that of deposition, we pro- nounce the air dry. It ought here to be observed that the sensation of dryness or wetness does not depend upon the absolute amount of aqueous vapour present in one cubic foot of air. For if the temperature be very low, although the air may not contain much aqueous vapour, yet this vapour may approach very nearly to the maximum amount which can be retained at the temperature, and the air will be pronounced wet. But if the very same mixture of air and vapour be heated up many degrees, the vapour will represent only a small fraction of the total amount which can be retained at the higher temperature, and hence it will feel very dry. If this high temperature be produced by a stove, it may even be necessary to place near the stove a vessel containing water in order to increase the amount of aqueous vapour present in the air. We see now what is meant by the dryness or wetness of the air, and all that remains is to express it numerically. This is done by the conception of relative humidity, which may be thus denned. Relative humidity is the fraction expressing the ratio between the tension of vapour actually present in the air at a given temperature and the greatest amount of vapour which it can contain at that tempe- rature. The greatest amount, representing complete satu- ration, is generally reckoned equal to 100, and on this principle 50, 40, 30, &c. will denote that the air contains 50, 40, 30, &c. per cent, of the maximum amount which can be contained at that temperature. 153. The weight of vapour present is another object of 140 CHANGE OF STATE. interest. In order to know completely the state of the air, it is necessary to know the weight of vapour present in a given volume of air, and also the entire weight of a given volume of air, or its specific gravity. This last element is necessary on another account, for a body weighed in air is lighter than if weighed in vacuo by the weight of its own bulk of air; in very delicate weighings, therefore, it is necessary to find the exact weight of the air displaced by the body ; and in order to obtain this information it is not sufficient to know the temperature and pressure of the air, but we must also know the weight of vapour contained in a given volume of air. 154. Having now mentioned the objects sought in hygro- metry, let us proceed to describe shortly the various instru- ments made use of in this science. We may state at the commencement that there are various means of ascertaining in a general way the dryness or wetness of the air. We may, for instance, use some substance which has a great affinity for water and readily deliquesces. Such a substance, if the air be very dry, will remain a long time comparatively unaffected, but if the air be moist it will rapidly deliquesce. In the next place, various substances have the property of becoming elongated when moist and of contracting again when dry; a hair, for instance, possesses this property, and Saussure has used it in his hair hygroscope. Other bodies, such as catgut, untwist when moist and twist when dry; and a toy has been made in which there are two figures, a man and a woman, suspended by catgut in such a manner that the man comes out when the air is wet and the woman when it is dry. All these methods, however, indicate rather than measure the hygrometric state of the air they are hygroscopes rather than hygrometers and we proceed from these to in- struments by which the state of the air with regard to mois- ture may be determined with precision. PRODUCTION OF VAPOUR AND ITS CONDENSATION. 14! 155. Dew-point instruments, hygrometer. This instrument (Fig. 30) is composed of two glass bulbs. The one A is more than half filled with ether, and contains a delicate thermometer plunged in the ether; the space above is void of air and of everything but the vapour of ether. The bulb B is covered with some fine fabric, such as muslin, upon which ether is dropped ; the evaporation of the ether produces intense cold, in consequence of which the ether Daniell's dew-point Fig- 30- vapour inside B is rapidly condensed, and of course the ether in A as rapidly evaporates. The evaporation of the ether at A cools the bulb until the air in contact with it sinks below the dew-point. Dew is therefore deposited on the outside of A, which is made of black glass in order that this deposition may be more readily observed. At the moment of deposition the thermometer in A is read. When the dew disappears, as the temperature rises, the same thermometer is also read, and the mean of these two readings is taken to indicate the dew-point. The thermometer C gives the temperature of the air. 156. Regnault's dew-point hygrometer. Regnault has invented a dew-point hygrometer which is free from some of the objections to which Daniell's is liable. It consists (Fig. 31) of two tubes of polished silver having glass tubes fixed to them. The tube A is half filled with ether. It contains a thermometer /' with its bulb in the ether, and also a fine glass tube C open at both ends, the extremity C being open to the atmosphere, and the other open end being plunged below the ether of A. The bulb B also contains a thermometer /, the object of which is to indicate the tempe- rature of the air. There is a communication between the 142 CHANGE OF STATE. air in A and the tube DE, and to the end E of this tube is attached an aspirator. By means of this aspirator the air from A is drawn through the tube DE, and its place supplied by new air entering at C and bubbling up through the ether. This continual cur- rent of air passing through the ether causes it to evapo- rate rapidly, and a diminution of temperature is thus pro- duced, until at last dew is deposited on the polished sil- ver of A ; the exact moment of deposition may easily be observed, and if the tem- perature of / ' be immediately noticed, we obtain the dew- point with great exactness, since the agitation of the ether renders it certain that the temperature of this thermo- meter is precisely the same as that of the polished silver. The moment of the disappearance of the dew may also be noted, but we have not in this case the same certainty that the thermometer and the polished silver are of the same temperature. 157. Wet and dry bulb hygrometer. This instrument was devised by Mason, and consists of two thermometers (Fig. 32) placed alongside of each other, one having a dry bulb and the other a bulb covered with muslin, kept moist by an arrangement similar to that in the figure. Owing to the evaporation from the latter its temperature will be generally below that of the former, and this difference will be greatest when the air is very dry, while in a very wet atmosphere the Fig. 31. PRODUCTION OF VAPOUR AND ITS CONDENSATION. 143 two temperatures will nearly coincide; the reason of this being that evaporation (Art. 121) is more rapid in dry air. It might at first sight ap- pear that the difference be- tween the two instruments would depend, not only on the dryness of the air, but also upon its velocity, since we have seen (Art. 121) that agitation of the air is favour- able to evaporation. Unques- tionably the withdrawal of heat by evaporation is greater when there is a current of air, but then it must be remembered that the difficulty of keeping a thermometer at a tempera- ture below that of the air is increased by the same cause and very nearly in the same proportion. This arrangement may be advantageously employed as a simple method of ascertaining the hygrometric state of the air with considerable accuracy, and for this purpose the fol- lowing formula, devised by Dr. Apjohn, is employed. Let/' denote the maximum elasticity of vapour correspond- ing to the temperature of the wet thermometer, and/" the elasticity of the vapour present in the air which it is wished to find. -Also let d denote the difference in Fahrenheit degrees between the two thermometers, and let h be the height of the barometer : then d h Fig- 32- 144 CHANGE OF STATE. for temperatures of evaporation above 32 Fahr., and d h / ^ / - 9 6 X 3o for temperatures of evaporation below 32 Fahr. Having found/"", or the elasticity of the vapour present in the air, we have only to look in our table for the temperature of which the saturation elasticity is f" in order to obtain the dew-point. Now it has been found, as the result of numerous experiments, that the dew-points obtained by this simple method agree very well with those determined by direct observation with Daniell's or Regnault's dew-point hygrometer. 158. Weight of vapour present in air. Specific gravity of air. We can easily calculate the weight W of a litre of dry air at temperature /C, and of elasticity P milli- metres, by the formula (see Arts. 136, 149) P T W= 1.293187 grm. x - x 760 i + .00367 x/ In like manner if we wish to know the weight W of a litre of aqueous vapour at temperature /' and elasticity P', we have (Art. 149) W = 0.623^ x 1.203187 grm. x ~^ x -' 760 i + .oo367x/ Suppose now it is wished to know the weight of one litre of air at temperature i5C, and pressure equal to that of 750 millimetres of mercury reduced to oC at Paris, the dew point being ioC. By Table III., at the end of this work, we find that the vapour pressure corresponding to ioC is 9.165 millimetres. Hence 740.835 millimetres will represent the pressure of dry air, and 9.165 millimetres the vapour pressure at the time of PRODUCTION OF VAPOUR AND ITS CONDENSATION. 145 observation. Now the weight of the dry air in one litre will be ^=1.203187 grm. x ^i^-^x 2 =1.10480 erm. : 760 i + . 00367 x 15 also the weight of the vapour in one litre will be W' = 1.293,87 gnn.x. 6235 x^ x 1+QQ l 67xl5 =0.0092. grm. Hence the whole weight of one litre of air will be 1.20401 gramme. 159. Correction for weighing in air. This will be best understood by an example. Suppose, for instance, that a substance of the approximate specific gravity 2.5 weighs 100 grammes in the air of which the weight was determined in last article, and that the approximate spe- cific gravity of the weights against which it is compared is 9.0. Now since the specific gravity of the substance is 2.5, we see from Art. 76 that the weight of a cubic decimetre or litre of the substance will be 2.5 kilogrammes, or 2500 grammes; and hence, since it only weighs i oo grammes, its volume will 100 be - = .04 litre. 2500 In like manner the volume of the weights against which it is weighed will be - = .oi litre. 9000 The weight of air displaced by the substance will there- fore be i. 204 gramme x .04 = .04816 gramme, and that displaced by the weights will be .01324 gramme, nearly. Hence the substance will weigh heavier in vacuo than in air by .04816 gramme. In the next place it must be remembered that the real weight of the body in air is somewhat less than i oo grammes, L 146 EFFECT OF HEAT UPON for the weights against which it is balanced denote 100 grammes in vacuo, and hence in air they will denote 100 .01324 = 99.98676 grammes, nearly. Therefore 99.98676 + .04816 = 100.03492 grammes will be the true weight of the body. CHAPTER VIII. Effect of Heat upon other Properties of Matter. 160. In what has preceded we have investigated the effects of heat upon bodies, chiefly as regards their volume and condition ; but this agent affects bodies in many other ways, and to these we shall now allude : but in the first place it may be well to recapitulate very shortly the leading results of the preceding chapters. We have seen that as the temperature of a solid rises it almost invariably expands in volume, and also that the co- efficient of 'expansion is greater at a high temperature than at a low one. If we continue to heat the solid it will ultimately assume the liquid state. In some bodies this change of state takes place very abruptly, but in others very gradually, so that they require a very considerable range of temperature in order to complete the change and become perfectly liquid. Sealing-wax is an example of the latter class, and ice probably of the former. In many cases there is an increase of volume as a body passes from the solid to the liquid state, but in others, such as ice, there is a considerable diminution. In all cases a OTHER PROPERTIES OF MATTER. 147 quantity of heat is rendered latent by the change. When the liquid state has been completely assumed any further increase of temperature will generally increase the volume of the liquid also. The coefficient of increase of volume is greater in liquids than in solids, and, just as in the case of solids, it is greater at a high temperature than at a low one. If we continue to heat the liquid it will ultimately assume the gaseous state, and during the process of change a great quantity of heat will be rendered latent, and a very consider- able expansion will under ordinary circumstances take place. There is some reason to think that, just as in the previous case so here, the state of a perfect gas is not instantaneously assumed, and that a vapour in contact with the liquid which produces it is not a perfect gas. If however this vapour, separated from the liquid, be allowed to expand in volume while its temperature is not diminished, it v will approach more and more to the state of a perfect gas. 161. We shall afterwards see, when we come to treat of the conduction of heat, that the thermal conductivity of a body becomes lessened as its temperature increases : and, under the head of specific heat, we shall also find that this quality of a body becomes altered by change of temperature. In the meantime let us endeavour to shew how the other properties of a body are altered by increase of temperature. EFFECT OF TEMPERATURE UPON REFRACTION AND DISPERSION. 162. One of the first experiments on this subject was that made by Jamin, who gradually, cooled down water to the freezing point, and found that as it cooled its index of re- fraction went on gradually increasing even after the point ol maximum density (4C) had been reached. This observation was afterwards confirmed by Messrs. Dale and Gladstone, who however found that the reversion at 4C of the be- L 2 148 EFFECT OF HEAT UPON haviour of water was not without influence on the refrac- tion, and the following table exhibits the result of their inquiries regarding the refractive index of water at different temperatures. Temperature of the water. Refractive index for line A of the solar spectrum. Refractive index for line D of the solar spectrum. Refractive index for line H of the solar spectrum. oC i 2 3 4 6-5 9 ii 32913 32913 32913 .32902 .32882 .32879 1-33374 I.33367 I-33356 1.33342 1-34377 1-34377 1.34366 1.34366 1-34337 I-3433I Messrs. Gladstone and Dale have since examined a great many different liquids ; their mode of research being to use the liquid as a fluid prism by which to obtain a solar spectrum; and they have found 1 . That the refraction uniformly diminishes as the temperature increases. 2. That the solar spectrum given by the substance diminishes in length as the temperature increases. EFFECT OF TEMPERATURE UPON THE ELECTRICAL PROPERTIES OF BODIES. 163. Thermo-electric currents. It was discovered by Seebeck that if a circuit composed of two different metals soldered together have one of* its junctions heated, an electric current will be produced. Thus in Fig. 33, if the lower plate be made of bismuth and the sides and upper plate of copper, and if one of the junctions be heated, then a current of electricity will be made to circulate. The direction of this current will be represented by the arrow-head, that is to say, OTHER PROPERTIES OF MATTER. 149 there will be at the heated junction a flow of positive elec- tricity from the bismuth through the copper to the cold junction. The existence of this current may be easily rendered evident, for we have only to place the compound circuit with its length in the magnetic meridian, so that a mag- netic needle inside will take the direction C C, when by heating the junction C by means of a lamp the north pole of the needle will be deflected as in the figure. The current so produced is called the thermo- electric current. 164. Thermo-electric series. If a compound circuit be made with any two metals in the following list, the positive current will go across the heated junction from the metal nearest the top to that nearest the bottom of the list : Bismuth Silver Nickel Zinc Lead Iron Tin Antimony Copper Tellurium. Platinum It will be seen that bismuth and antimony are nearly at opposite extremities of this table, and as both these metals are easily obtained they are generally employed in thermo- electric combinations. 165. Thermo-pile. It was formerly assumed that the quantity of electricity set in motion by heating the junction of a compound circuit is proportional to the difference in 1 5 o EFFECT OF HEAT UPON temperature of the two junctions. It will be afterwards seen (Art. 1 66) that when the heating is very great this law does not hold, but if the junction be only heated slightly it will represent the truth. In this latter case, if we can find means to measure the strength of the current we obtain at the same time a measure of the difference in temperature of the two junctions, and thus the combination will be equivalent to a differential thermometer. In adapting a thermo-electric arrangement to this purpose three things have to be borne in mind, if great delicacy be desired. In the first place, it will be necessary to produce as strong an electric current as possible; in the second place, we ought to render this current as effective as possible in deflecting a magnetic needle; and in the third place, we ought to magnify the smallest motion of the needle so as to make it visible. In order to produce as strong a current as possible, a number of pieces of antimony and bismuth are soldered together, as in Fig. 34, and when the heat is applied above we have the united effect of all the cur- rents at the hot junctions passing though the circuit, including the galvanometer, in the direction of the arrow-heads. In practice a square block, con- taining altogether 25 couples of bismuth and antimony, is gene- rally employed such an arrange- ment is called athermo-pile. This instrument is however incomplete without a galvanometer, and we shall now shortly describe Professor William Thomson's reflecting galvanometer, which is admirably adapted for use with the thermo-pile. In this galvanometer a small magnet Fig- 34- OTHER PROPERTIES OF MATTER. 151 m (Fig. 35) acts as the magnetic needle; it is attached to the back of a small flat circular mirror which is delicately suspended by a fine thread. The needle is surrounded by coils of the wire which conveys the current of the thermo-pile, and when the current is passing, the needle and attached mirror will of course be deflected out of their previous position. But the needle m is under the influence Flg- 35 ' of the earth's magnetism, and under ordinary circumstances a very weak current coming from the thermo-pile would be able to turn this needle only a very little distance out of the magnetic meridian before it would be stopped by the earth's magnetic ' force tending to bring it back. A rather large magnet M (Fig. 36 *) is however placed in Fig- 36. * This figure is due to the kindness of Mr. C. Becker of Messrs. Elliott, Brothers, London. 152 EFFECT OF HEAT UPON such a position as to counteract as nearly as possible the earth's magnetic force upon the needle m which is inside G. The consequence of this arrangement will be that whereas without M the earth's magnetic force would overcome the current when the magnet m had been deflected but a little way ;. now, by means of M, the earth's magnetic force on m being very nearly counteracted, the magnet m will be- have as if it were astatic, and will describe, when acted on by the current, a very much larger arc before it is checked. In the next place, a small motion of m is rendered visible by the following means. Since the needle is attached to the back of a freely-suspended mirror, any motion of the needle will of course be followed by an angular deviation of the mirror. Now the light from an illuminated slit r, having first been made to pass through a small lens in the galvano- meter G, falls upon the mirror and is reflected back in the line Gs' so as to throw an image of the luminous slit upon a graduated scale. It is evident from this arrangement that a comparatively small change in the plane of the mirror will produce a very large change in the position of the luminous image on the scale. Also, from what has been said it will be inferred that this instrument combined with the thermo- pile will have all the requisites of a very delicate differential thermometer. For, in the first place, by means of a pile with a number of pairs we produce a strong current of electricity ; secondly, the needle is very sensitive to the in- fluence of this current ; and thirdly, small motions of the needle are magnified so as to be rendered easily visible, being at the same time strictly proportional to the strength of the current which causes them. When used to indicate the presence of radiant heat the pile is generally furnished with a brass cone c, the interior of which is polished ; by which means not only the heat which reaches the pile itself OTHER PROPERTIES OF MATTER. 153 but that which falls upon the cone is ultimately reflected upon the face of the pile, and its sensibility is thereby greatly increased. In the figure there are two brass cones, but in the experiment we are describing only one of these is exposed to the source of heat, the other being shut by a brass cover. The junctions of the pile are also usually covered with lamp-black, a substance which absorbs every kind of radiant heat. So delicate may an arrangement of this description be made, that if a substance be presented before the cone c one degree Fahr. hotter than the pile itself, the mere radiation from this substance, by very slightly heat- ing the. one face of the pile, will in some instruments cause a change in the position of the reflected luminous image equal to 50 or 60 divisions of the scale. On account of its great delicacy an arrangement of this kind is eminently adapted to researches on radiant heat as we shall see when we come to that branch of our subject. ..:.? 2 166. Thermo-electric inversions. It was at first sup- posed that the current produced by heating one junction of a compound-circuit would prove to be proportional to the difference in temperature between the two junctions. This, however, is not the case. Gumming was the first to shew that in a circuit of certain metals, if one junction is kept cool while the other is gradually raised in temperature, the current, instead of going on regularly increasing, begins to diminish, then comes to a stop, and ultimately sets in the opposite direction. This observer found that if gold, silver, copper, brass, or zinc wires be heated with iron the direction of the current becomes changed at a red heat. 167. Pyro-electricity. Certain minerals when heated acquire electrical properties. One of these is tourmaline, in which this effect of heat was originally discovered by ob- serving that when brought into contact with hot ashes it first 154 EFFECT OF HEAT UPON attracted and then repelled them. It was found by Canton that it is not the absolute temperature but change of tem- perature which renders a tourmaline electric. Suppose, for instance, we have a tourmaline whose poles we call A and B. If this tourmaline be kept sufficiently long in a medium of constant temperature it will exhibit no electric manifestations. If it be transferred into a warmer medium, A will exhibit positive and B negative electricity ; while if transferred into a colder medium, A will exhibit negative and B positive electricity. A similar property is possessed by other crystals, and Haiiy was the first to remark that those crystals are pyro- electric which are deficient in symmetry. 168. Effect of temperature upon the electric con- ductivity of bodies. Pure metals. This subject was first studied by Sir H. Davy, but the latest and probably the most accurate research is that of Dr. A. Matthiessen and M. Von Bose, who have obtained the following result : Electric conductivity. Name of substance. At oC. Silver at oC = 100. At 1C Silver at oC = 100. >oC. Silver at iooC = 100. Silver (hard drawn). . . . Copper (hard drawn) . . Gold (hard drawn) .... Zinc 100.00 99-95 77.96 29.02 23.72 12.36 8.32 4.76 4.62 I.24.S, 71.56 70.27 55-9 20.67 16.77 8.67 5-86 3-33 3.26 o.8?8 100.00 98.20 78.11 28.89 23-44 12.12 8.18 4.65 4-55 1.227 Cadmium Tin Lead Antimony N Bismuth . . We thus see by comparing together the first and third columns of this table that the proportion between the electric conductivity of the different metals is very nearly the same at iooC as at o, while by the second column we see that the OTHER PROPERTIES OF MATTER. 155 decrement between o and 100 is nearly 29 per cent, for each metal. A later research by Dr. Matthiessen and C. Vogt shews that thallium and iron are exceptional in their behaviour, and that for thallium the decrement between o and iooC is 31.42 per cent. In like manner the decrement for pure iron between the same limits was found to be 38.26 pef cent. 169. Liquids. Marianini was the first to shew that an increase of temperature exalts the electric conductivity of liquids, and his results have since been confirmed by Becquerel, who made experiments on solutions of sulphate of copper and sulphate of zinc, and on the nitric acid of com- merce. From these it appears that a difference of from 20 to 3oC suffices to double the conductivity of these liquids, probably by facilitating electrolysis. 170. Bad conductors. Heat converts many insulating solids into conductors by making them liquid, and of these ice is a notable example, which insulates when solid, but conducts electricity in the fluid state ; also glass, resin, and wax, which insulate at ordinary temperatures, become con- ductors at a temperature sufficient to soften them, and their conductivity is still more increased when they assume the liquid state. There are, nevertheless, many substances in which igneous fusion does not develope conducting power, and of these sulphur, phosphorus, and camphor may be quoted as examples. Finally, the loss of electricity in dry air increases very sensibly with the temperature. EFFECT OF TEMPERATURE ON MAGNETISM. 171. If we heat a magnetised bar of hard steel we produce a diminution in its magnetism, but if the heating be not too 156 EFFECT OF HEAT UPON great, when again cold it will recover its former state. In such a magnet, therefore, the intensity will be a function of the temperature. But if this bar be brought to a white heat it will totally lose its magnetism, and will not recover it when again cooled. In like manner a soft iron bar when it is brought to a red heat is no longer attracted by the magnet Nickel also ceases to be magnetic at the temperature of boiling oil, or about 600 Fahr., and cobalt at an extremely high tem- perature. EFFECT OF TEMPERATURE ON CHEMICAL AFFINITY. 172. An increase of temperature in a great many instances promotes chemical combination. Thus phosphorus, if slightly heated in oxygen or air, takes fire; and, generally 'speaking, a large number of bodies which do not combine together at ordinary temperatures do so when the temperature is in- creased. Sometimes, however, heat promotes chemical decomposi- tion, especially when the products of such decomposition ar$ gaseous. Thus, if limestone be heated it parts with its car- bonic acid gas and is converted into lime. Many substances, too, which possess little chemical stability, decompose on the application of heat, often with explosive violence. The terchloride of nitrogen, and the various fulminates, are examples of this class. The effect of heat upon the solvent powers of bodies has been already alluded to. EFFECT OF TEMPERATURE ON OTHER PROPERTIES OF MATTER. 173. It is well known that an increase of temperature alters the behaviour of a liquid in a capillary tube. M. Wolf and also M. Drion have lately made some interesting experi- OTHER PROPERTIES OF MATTER. 157 ments on this subject, in which the capillary tubes containing the liquids were heated very considerably under pressure. M. Drion has come to the following conclusions : 1 . That for the liquids studied the , capillary meniscus remains concave until the moment of complete evaporation ; its form at that instant being plane. 2. That for the same liquids the capillary ascension and curvature diminish as the temperature rises, until the moment of complete conversion of the liquid into vapour. An increase of temperature affects also the extensibility of bodies. Wertheim has made numerous experiments on this subject, and he finds that in general metallic threads offer more resistance at a low than at a high temperature to a force tending to elongate them, so that the proportional elongation produced by a given weight is smaller in the first case than in the second. To this law, however, iron and steel present an ex- ception, their resistance to elongation augmenting from i 5 to iooC, while at 200 it is not only smaller than at ioo c C but sometimes even smaller than at ordinary temperatures. In like manner the tenacity of a metallic wire, as estimated by its breaking charge, is altered by increase of tempera- ture. This subject has been studied by Wertheim and also by Baudrimont, by whose researches it appears that the effect of heat is to some extent irregular, tending some- times to diminish and sometimes to increase the tenacity if one does not go above 2OOC. At a red heat, however, the tenacity of iron is very much diminished. According to the experiments of M. Grassi the com- pressibility of water under pressure diminishes as the temperature increases, while heat, on the contrary, appears to augment the compressibility of ether, alcohol, and chloroform. 158 EFFECT OF HEAT, &C. In like manner the cohesion and the hardness of bodies is diminished by heat, their crystalline form is altered, and indeed tljere is no property of matter that is not affected by this agent, although it is only in a few cases that its effects have been accurately examined. BOOK II. ON THE LAWS WHICH REGULATE THE DISTRIBUTION OF HEAT THROUGH SPACE. CHAPTER I. Radiant Heat. (Preliminary^) 174. IT has already been stated on a previous occasion (Art. 5) that a body parts with its heat in two ways, namely, 1 . By contact with a cold body, 2. By radiation through space; and in order to render this distinction very evident it is only necessary to mention a familiar instance of each method. When one end of a poker is heated in the fire the heat is gradually conveyed to the other end through the substance of the poker. This is an instance of communication of heat by contact, the cold particles receiving heat from the warmer ones next them, and in their turn conveying it away to still colder particles, until after a considerable time has elapsed it reaches the other extremity of the poker. Now in this case it is evident that the particles at the cold end are not immediately and directly heated by those at the hot end, but only through the agency of the intervening particles, and the great characteristic of this process is its l6o RADIANT HEAT. (PRELIMINARY.] exceeding slowness. It is very clear that this cannot be the method by which we receive heat from the sun, and indeed we have no reason to think that there is matter capable of retaining heat between the earth and our luminary. The effect in this instance is certainly not due to the heating of the intervening regions, but, on the contrary, it is as powerful in a very cold atmosphere as in a warm one, and may even be felt behind a screen of ice. We know, too, that light, and doubtless also heat, reach us from- the fixed stars, although these bodies are vastly more distant than the sun. It is this heating emanation which we term radiant heat, and in its character and distribution it is subject to certain laws, which we shall now proceed to describe. In the first place 175. Radiation of heat takes place in vacuo as well as in air. For it takes place between the sun and the earth and between the fixed stars and the earth, and we have no reason to think that all space is filled with some kind of air. 176. Radiation takes place equally on all sides. If a sphere be heated and very delicate thermometers be placed on diiferent sides of such a sphere at equal distances from the centre, they will always give the same indications. Such a sphere will also appear equally luminous from all sides. 177. Radiant heat traverses void space in straight lines and with the same velocity as light, that is to say, at the rate of about 190,000 miles in a second. The best proof of this statement is derived from the great probability, if not certainty, that heat and light are varieties of the same physical agent. This will be investigated at a subsequent part of this book. 178. Radiant heat is capable of passing through RADIANT HEAT. (PRELIMINARY.) l6l certain substances without sensibly heating them. If a plate of rock salt be placed between us and the sun, we shall yet feel to a very great extent the effect of his beams ; few of his rays will be stopped, and the screen will not be heated to a perceptible extent. We may therefore infer that radiant heat passes through certain substances without being perceptibly absorbed or heating them to a sensible extent. It is, however, probable that no substance is perfectly transparent with respect to heat (or diathermanous, as it is termed), and that all bodies are heated to a greater or less extent by the passage through them of calorific rays. 179. Radiant heat is probably not a substance emitted by a hot body, but an undulatory motion conveyed through a medium which pervades all space. Apart from the difficulty of conceiving space to be traversed by excessively minute particles all moving with the uniform velocity of 190,000 miles per second, the follow- ing experiment has been performed by Mr. Bennet. The light and heat of the sun have been concentrated upon a substance swung so delicately that the slightest momentum would cause it to change its position, but no such change has been observed. If we infer that light and heat do not consist of particles emitted by a hot body, our natural al- ternative is to suppose that they are undulations of a medium pervading space. This hypothesis furnishes by far the best explanation of many very curious phenomena in light and heat, and is now very generally received. It will be convenient here to define the various terms con- nected with this hypothesis. If a stone be dropped into a pool of water, a series of undulations consisting of crests and hollows succeeding one another will spread outwards from the centre of disturbance. Now the distance between two contiguous crests or between two contiguous hollows is M 1 62 RADIANT HEAT. (PRELIMINARY.} termed the wave length, because in this distance is embraced the whole variety of motions which together constitute a wave. When the ocean is agitated by a storm we have also waves, but here the wave length is obviously much greater than in the case above mentioned. We thus see that the same substance may be the medium of propagating waves of different lengths. In these instances the direction of disturbance is up and down, while the direction of propagation is horizontal; and thus the displacement of a particle is in a direction at right angles to that of trans- mission of the wave. In air we have another substance capable of conveying undulations of different wave lengths. These undulations constitute musical sounds, the wave length defining the pitch of the note. Thus if one note be an octave lower than another, its wave length will be double that of the other. The waves of sound are, however, different from those of water, inasmuch as they are not waves made up of crests and hollows, but of condensations and rarefactions succeeding one another ; in fact, the direction of displacement of the air instead of being at right angles to that of transmission of the wave, is in the same direction. We have thus two varieties of waves 1. Waves of crests and hollows, where the direction of displacement is perpendicular to that of transmission. 2. Waves of condensation and rarefaction, in which the direction of displacement coincides with that of transmission. Now whether light and heat rays consist of undulations of the first or of the second description, in either case we are entitled to expect that difference of wave length will denote some important difference in the quality of the ray. There are many considerations which induce us to imagine that difference of colour is denoted by difference of wave length, and that red, yellow, orange, green, blue, indigo, and RADIANT HEAT. (PRELIMINARY.) [63 violet have all their peculiar wave lengths. There are other considerations which induce us to imagine that these wave lengths are very small, being for violet rays no longer than .0000167, an d for red rays .0000266 of an inch, while for heat rays we shall afterwards see that the wave length is some- what larger than for red rays. But again, there are strong reasons for believing that waves of light consist of crests and hollows, while sound waves con- sist of condensations and rarefactions. There is this im- portant distinction between the two cases. If we hold a string somewhat tightly in a horizontal direction and strike it from above downwards, we perceive speeding along it a crest and hollow wave for which the direction of displacement is in a vertical plane. And if we strike it from the side we perceive a similar wave, for which the direction of displace- ment is in a horizontal plane. We can have thus two sets of crest and hollow waves proceeding in the same direction along the string, the plane of vibration of the first being at right angles to that of the second ; but it is evident that we can have no such distinction in waves of condensation and rarefaction. Now when the vibrations of a crest and hollow wave are always confined to the same plane, that wave is said to be polarized. Thus in a wave proceeding in a horizontal direction if the vibrations of the particles be confined to a vertical plane, the wave is polarized; and if they be confined to a horizontal plane it is also polarized, but in a direction at right angles to the former : but if these vibrations have no reference to any particular plane, then the wave is unpolarized. Now there are certain processes by which a ray of ordinary light may be broken up into two rays that appear to have reference to planes at right angles to one another. By such a process the ray is said to be polarized. And this fact entitles us to assume that waves of light are crest and M 2 164 RADIANT HEAT. (PRELIMINARY.) hollow waves and not waves of condensation and rarefaction, since these last from their nature cannot have a reference to any particular plane. ISO. The intensity of radiation varies inversely as the square of the distance from the radiating body. It would appear that this law ought theoretically to hold good whether we consider radiant heat to be particles ejected by a heated body, or to be an undulatory movement of an etherial medium proceeding outwards from this body. In either case the amount of vis viva which at one moment, and at the distance (say) of one mile from the centre, covers the surface of a sphere of which the radius is one mile, will at another moment and at the distance of two miles from the centre cover the surface of a sphere of which the radius is two miles ; that is to say, the same amount of vis viva or heat will have spread itself over a surface four times as large, and hence the amount of vis viva or heat corresponding to unit of area, that is to say the intensity, will be diminished four times, and will therefore vary inversely as the square of the distance. The following ingenious experimental verification of this law was first given by Melloni. Suppose, in the first place, that we have a large red-hot wall before us and that we view it through a small tube, blackened in the inside, held close to the eye. The opening of this tube furthest from the eye will appear to be red hot, and it will appear so whether we ap- proach the eye and tube close to the wall or withdraw them to a distance, always provided that the wall be large enough to fill up the field of view from the eye. If the eye and tube be far from the wall we embrace in the field of view a much larger extent of the wall, but we view it from a greater distance, so that what is gained in extent is lost in distance, seeing that in this arrangement the same amount of light reaches the eye at all distances. Now we know that the REFLECTION, etc. OF RADIANT HEAT. 165 extent of heated surface viewed in this manner varies directly as the square of the distance, therefore we see that rate of di- minution must be inversely as the square of the distance, Melloni applied a tube of this kind not to the eye but to a thermo-pile, (which is very sensitive to heat rays, just as the eye is to those of light,) and he found that the indication of the galvanometer, and hence the amount of heat acquired by the pile, was the same whether the pile was near the hot wall or far from it, provided always that the wall was sufficiently large to fill up the field of view from the pile. CHAPTER II. Reflection, Refraction, &c. of Radiant Heat. 181. The laws of radiation which have been stated in the preceding chapter are sufficient to exhibit the great similarity between radiant light and heat, and even to render it pro- bable that both these effects are due to the same physical agent. Our belief in this is greatly strengthened by observing that the various phenomena of optics are reproduced in radiant heat, and it is to a consideration of these that the present chapter will be devoted. We shall mainly direct attention to the following properties of radiant heat 1. Reflection. 2. Refraction. 3. Absorption. 4. Polarization and double refraction. But, in the first place, we shall make a few preliminary remarks on the spectra of heated bodies. 1 66 REFLECTION, d-c. OF 182. Newton was the first to prove that a ray of sunlight really contains, blended together, a very great number of simple rays, each exhibiting a different colour; and his funda- mental experiment may be shortly described as follows. Let us take a glass prism, and place it in a vertical posi- tion, and let a ray of sunlight strike obliquely against its side. As this ray passes through the prism it will be bent in such a manner that its line of exit will differ very much in direction from that of incidence. But, besides this, each simple coloured ray of which the compound ray is composed will be bent by the prism in a different manner, so that the rays which entered the prism in the same direction will leave it in different directions, and we shall thus obtain in a sepa- rated condition all those variously coloured rays which to- gether form a beam of white light. It is easy now to shew what is meant by the term ' Spectrum/ Suppose, for in- stance, that by an arrangement similar to the ordinary photo- graphic camera we were to throw upon a screen the image of a vertical line of light. Under ordinary circumstances this image would be a vertical line, but if a prism were inter- posed in the path of the rays each constituent of the light from the slit would be bent by it in a different direction, and we should have the vertical image of the slit due to one of these constituent rays thrown upon one part of the screen, and that due to another constituent ray thrown upon another part, and so on. We should thus obtain not one image of the slit but a very great number of these contiguous to one another, so as to form an oblong space illuminated by various colours. This space is called the spectrum of the line of light, and if the light be that of the sun we thus obtain the solar spectrum. 183. This oblong space, we have observed, is differently coloured throughout. The following diagram (Fig. 37), in which the left side represents the least and the right the most RADIANT HEAT. l6 7 refrangible rays, will give an idea of the colour and com- parative luminosity of the different parts of the solar spec- LIGHT SPECTRUM Curve 'oflntens itu of Liyht I Or- \Vel\ Red \ if .Green- Blue i ancfe\ low-. Indufo\ Violet Fig- 37- trum. The ordinates of the curve denote the luminosity for each part, and it will be seen that the greatest intensity of light is in the yellow. If now we obtain the solar spectrum by means of a prism, or set of prisms, which we are sure do not absorb any of the rays, or do so only to a very small extent, (and for this pur- pose we must use rock salt,) and if we estimate the heating effect of each portion of the spectrum by means of a thermo- pile or otherwise, we shall have an exceedingly curious result, which is roughly sketched in the following diagram (Fig. 38). HEAT SPECTRUM Dcurk Heat Rcuys Visible Spectrnjon Chemica I fiays. Fig. 38- From this it appears that the maximum heating effect is a good deal beyond the red, and that the rays which produce it are invisible to the eye. If our instrument for measuring heat be delicate enough, we shall also find that the heating effect ex- 1 68 REFLECTION, Ac. OF tends to the right as well as to the left of the visible spectrum, although in the former direction it is extremely feeble. Besides the illuminating and heating powers of rays they have a third property, namely that of producing chemical action. Chloride of silver, it is well known, becomes black- ened under the influence of light, and it is by making use of this property that we are enabled to obtain photographic pictures of bodies. But the action of certain rays upon chloride of silver is much more energetic than that of others; this being most intense for the violet, or more refrangible rays, and even ex- tending much beyond the visible extremity of the spectrum towards the right. We have thus three things 1. A luminous spectrum with a maximum of light in the yellow. 2. A heat spectrum with a maximum to the left of the visible spectrum. 3. A chemical spectrum with a maximum probably in the violet, and a great intensity of chemical action beyond the violet, to the right. 184. If we now proceed to consider the spectra of other luminous solid bodies, we shall find that these are very analogous to that of the sun, except in respect of dark lines, which we may for the present dismiss from our con- sideration. If the temperature of the source be high, we have, besides a great deal of dark heat, a good amount of luminosity and a smaller amount of chemical action ; but as the temperature decreases we perceive a very considerable diminution in the amount of light and a still greater falling off in the chemical rays, until below a red heat both chemical action and light have entirely disappeared and the whole of the radiation consists of dark heat. RADIANT HEAT. 169 Thus if the temperature of the source be low, the whole radiation is of the nature of that portion of the solar spectrum which lies in the diagram to the left of red. (We shall afterwards see what experimental grounds we have for this assertion.) If the temperature be moderately high we get in addition a little light, and if it rise still higher, a little chemical action, until, when it becomes very high, we have a good deal of light and somewhat less chemical action, but we have reason to think that in all cases the light and chemical action bear but a small proportion to the dark heat. 185. Dismissing in the meantime the chemical rays from our consideration we may separate radiant heat into two kinds, the first embracing those rays which by means of the prism can be separated from light and which lie to the left of the visible rays in the spectrum, while the second denotes that heating effect which accompanies light and which cannot be separated from it by prismatic analysis. With regard to these we must now answer the two following questions : 1. Is the dark heat beyond the red composed of rays similar in physical constitution to those of light ? 2. In the portion of the spectrum which is visible is the heating effect produced by the very same rays which produce the luminous effect, or are there two sets, the one heating and the other luminous, mixed together ? We shall best answer these questions by proceeding at once to state the various properties of radiant heat which have been experimentally proved, and then using these as a means of comparing together the two agents heat and light. REFLECTION OF HEAT. 186. Dark heat is capable of reflection. The follow- ing experiment will exhibit the reflection of heat. 17O REFLECTION, &c. OF Suppose that we have two concave metallic reflectors facing one another (as in Fig. 39), and let A be the focus Fig- 39- of the one and D that of the other. Let an iron ball, heated to a temperature somewhat below redness, be placed at A ; if we place a piece of phosphorus at D it will probably take fire, or if we place a thermometer there its temperature will rise much more than if we placed it in any other position in the neighbourhood. The reason is, that the rays which leave the ball A, such as AB, A C, are reflected at B and C from the polished metallic surface of the one mirror in parallel lines BE, CF, while at E and F these are again reflected by the other mirror in the directions ED, FD, and thus converge upon the point- D, the focus of that mirror. In the heating of the thermometer placed at D we have thus a proof of the reflection of dark heat from a metallic surface. Leslie has made numerous experiments with regard to the reflecting powers of bodies for dark heat. The following was the arrangement which he adopted at a time when the thermo-pile was yet unknown. In Fig. 40, m is a con- cave metallic mirror, and the source of heat is a cube containing hot water, the rays of heat proceeding from RADIANT HEAT. which would, if left to themselves, converge to a focus at f; but in consequence of a reflecting plate ab being Fig. 40. placed in their path their focus is at f. It is clear that if the plate ab be taken away and another plate substituted in its place which reflects only half as many of the rays which fall upon it, then the heating effect at f will be reduced to one-half of its previous amount; in fact, this heating effect will be proportional to the reflecting power of the surface ab. Leslie measured this effect by means of his differential thermometer, an instrument which we have already described (Art. 29). By this means he obtained not the absolute reflecting power of any body or the number of rays which it reflects out of every hundred which fall upon it, but only the comparative reflecting power of different surfaces. Calling that of brass 100, he obtained by these means the following result Brass JOQ Lead 60 Silver 90 Amalgamated tin 10 Tin 80 Glass 10 Steel 70 Lamp-black o It will be seen from this list that metals which reflect light most copiously are also the best reflectors of obscure heat.. 172 REFLECTION, Ac. OF 187. The heat which belongs to light is reflected in the same manner as the light. M. Jamin has shewn that if we take certain elementary rays, or, which is the same thing, a certain small portion of the spectrum, the reflecting power of any substance with respect to the light of this portion will be as nearly as possible the same as its reflecting power for the heat. We thus obtain, the following table, in which any small difference between heat and light may be attributed to error of experiment. Green of the spectrum. Red of the spectrum. reflecting. Reflecting power for heat. light. Reflecting power for heat. light. Platinum. CQ 60 Zinc 65 62 60 t;8 Metal of mirrors Brass .. 5 8 62 6l 62 65 69 7* 72 188. Variation of the reflecting power with the angle of incidence. It has been proved by MM. de la Provostaye and Desains that the reflecting power of glass for heat increases very rapidly with the angle of incidence, and that the law which regulates this augmentation is, as nearly as we can perceive, the same as that which holds for light. These observers have also found that the reflecting power of metallic surfaces for heat varies very slowly with the incident angle, a peculiarity which metals also possess with regard to light. 189. Diffuse reflection of heat. MM. Provostaye and Desains, and also Knoblauch, have made experiments on this subject, and they find that as in the case of light some of the rays are scattered about by the surface and reflected in an irregular manner, so also with regard to heat there is a diffuse reflection or scattering about of the rays. The laws of this are not exactly known, but what is known tends to strengthen the argument in favour of the identity of light and heat. RADIANT HEAT. 173 190. As the result of the experimental researches made with regard to the reflection of heat, we find : 1. Dark heat in the same manner as light is reflected very copiously by metals. 2. Heat, whether reflected from a surface of glass or from one of metal, is subject to laws precisely similar to those of light, whereby the intensity of the reflected beam is con- nected with the angle of incidence. 3. Heat, in the same manner as light, suffers a scattering or diffuse reflection from the surface of bodies. 4. If we confine our experiments to a part only of the spectrum, we find that the light of this portion is re- flected by a surface precisely in the same manner as the heat. We are therefore disposed to conclude that, as far as reflection is concerned, dark heat is subject to the same laws as light, and also that, if we take any region of the visible spectrum, its illuminating and heating effects are caused by pre- cisely the same rays. REFRACTION OF HEAT. 191. When Sir W. Herschel first noticed that there was a heating effect beyond the red of the visible solar spectrum, this observation implied the refraction of heat. But Melloni was the first to prove experimentally that the heat which ema- nates from a non-luminous source is capable of refraction. His success in these experiments was due to two very important aids. In the first place, he found that a plate of rock salt allows almost every sort of dark heat to pass readily through it, while every other substance powerfully absorbs this kind of heat. By using a rock-salt prism he was thus sure that the heat would not be stopped by the substance of his prism. Furthermore, Nobili and Melloni were the first to employ 174 REFLECTION, d-c. OF the thermo-pile for investigations of this nature, and by an improved arrangement of this instrument the latter was enabled to detect the presence of an exceedingly small amount of radiant heat. (This instrument has been already described, Art. 165.) By means of these two important experimental adjuncts Melloni was able to render manifest the concentration of dark heat upon the focus of a rock-salt lens, and also to shew that it is bent by a rock-salt prism ; thus proving conclusively the refrangibility of such heat. Fig. 41. Fig. 42. The method of experiment is illustrated in Figs. 41 and 42. The subject was afterwards taken up by Professor Forbes, who shewed that the refrangibility of dark heat is inferior to that of the luminous rays. By a method founded on the total reflection of heat he obtained the following indices of re- fraction, the substance being rock salt. Indices of refraction. Heat from Locatelli lamp . . . 1.571 ., from incandescent platinum . 1.572 from brass at 700 Fahr. . . 1.568 Mean luminous rays 1.602. RADIANT HEAT. 1 75 It is important to compare this result with that obtained by Sir W. Herschel, who found dark rays beyond the red of the visible spectrum, and consequently less refracted than light. We thus see that dark rays of a less refrangibility than light belong alike to sources of heat of low temperature, and to those of high temperature, such as the sun ; the dif- ference being, as we have already remarked, that bodies of low temperature give out only dark rays, whereas those of high temperature give out luminous rays as well. Pursuing his researches on this subject, Professor Forbes found that the wave length of the heat rays was most probably considerably greater than that of the light rays, a result in accordance with the optical determinations of Fraunhofer and others, who have found the wave length of the red rays greater than that of the more refrangible rays of the spectrum. We thus see that both as regards refrangibility and wave length the dark spectrum appears to be the appropriate prolongation of the luminous one. , . ABSORPTION OF HEAT. 192. The discovery by Melloni, that rock salt is a body which transmits heat freely, sufficiently indicates that most substances which are transparent for light are not so with regard to heat. In the language adopted by scientific men this is expressed by saying that most substances are athermanous, and that rock salt is almost the only diather- tnanous substance, these two words corresponding to the terms opaque and transparent in the science of optics. There are two facts regarding the absorption of heat that may with advantage be discussed here. In the first place, when the heat ivhich radiates from a hot body has passed through one screen it is more easily able to penetrate another screen of the same material. This was originally observed by De la Roche, and his observations have since been abundantly Ij6 REFLECTION, &c. OF confirmed by Melloni, Forbes, and others. They have expressed it as a sifting of the radiant heat by its passage through the first screen; certain rays being stopped and only those allowed to proceed which are of a nature easily able to penetrate the material of the screen. It will be observed that this is quite analogous to the action of a red screen upon light, which stops the blue rays but allows the red to pass, nor will these red rays be much diminished by a second screen of the same material. There is thus exercised by solid and liquid bodies a selective absorption both for heat and light, in virtue of which certain rays are set apart to be stopped while certain others are allowed to proceed. It may be remarked that besides selective absorption of rays by substances there is probably also a more general absorp- tion, which may conveniently be kept separate from the former. We have some grounds for believing that very thick strata of air, water, glass, or any substance seemingly trans- parent, will ultimately stop light, possibly at a rate not greatly differing for the different rays. But to return to selective absorption. We have reason to think that this property, as regards both light and heat, is exceedingly marked in gases ; indeed the vapour of sodium is found to be quite transparent for every kind of light except for that from a salt flame, for which it is quite opaque, and Professor Tyndall has also observed a similar action of gases with respect to radiant heat. We remark, in the second place, that most substances, including those that are transparent for light, are generally opaque for dark heat of great wave length and small refrangibility. Rock salt has been mentioned as an exception, but even this is not perfectly diathermanous. Provostaye and Forbes have both found that it passes a smaller proportion of heat rays than of light rays, and the author of this work has attempted to shew that the rays RADIANT HEAT. 177 which it stops are those of very great wave length. Forbes has also shewn that transmission in general raises the index of refraction of the transmitted heat; in other words, a screen stops in preference those rays which have the lowest index of refraction or greatest wave length. But this rule, though very general, is not universal; for it has been found by Melloni and Forbes that smoked rock salt and mica, split by heat into a bundle of thin pellicles, pass in preference dark rays ; and by Tyndall that a solution of iodine in bisulphide of carbon has the property of completely stopping the light rays, while it allows dark heat to pass in great quantity. Tyndall found that a fluid lens formed of this solution and enclosed in rock salt will stop all the light from an electric lamp, but permit the dark rays to pass in sufficient abundance to produce incandescence. We shall on a future occasion return to the subject of absorption, which is a very impor- tant one. POLARIZATION OF HEAT. 193. We have seen that there is an analogy between light and heat as regards reflection, refraction, and absorp- tion; and it might be expected that the same should hold as regards polarization. Malus and Berard were the first to shew that the heat accompanying solar light is capable of polarization. In 1834 Professor Forbes took up the inquiry ; but before describing his experiments it may be well to describe the action of tourmaline and glass with respect to light. If a plate of tourmaline be cut with its plane surface parallel to the axis of the crystal, and if a ray of ordinary unpolarized light be allowed to fall upon it, it divides the ray into two parts, one polarized in the plane of the axis, and the other in a plane perpendicular to the axis, and the former of these is absorbed while the latter is allowed to pass. The light transmitted through such a plate will therefore be polarized in a plane perpendicular N 1 78 REFLECTION, Ac. OF to the axis of the crystal. If now a similar plate of tour- maline be placed behind the first, but with its axis at right angles to the axis of the first, then the light transmitted by the first will be absorbed by the second, so that the com- bination will be virtually opaque; if, however, we turn the second plate round until the axis of both plates coincide, then the combination will be transparent. Again, if a bundle of plates of glass or any similar substance, such as mica, be held together, and if a ray of light be allowed to strike obliquely at a certain angle upon them, part of this will be reflected back, and part will be transmitted through the plates. Now it is found that the reflected part is very nearly polarized in one plane, and the transmitted part in a plane perpendicular to that of the reflected light; and furthermore, if the reflected or the transmitted ray be again reflected or transmitted by a similar bundle of plates, but with its plane of incidence perpendicular to that of the first bundle, then the rays that have been reflected by the first bundle will not be reflected by the second, nor will those that have been transmitted by the first bundle be transmitted by the second. But if the plates are parallel, so that the planes of incidence coincide, then they will reflect or trans- mit the rays. Now if radiant heat be similar to light, we should expect phenomena similar to the above ; and accordingly Professor Forbes, by using two plates of tourmaline cut with their planes parallel to the axis, proved that there was a marked additional stoppage of heat (just as there is of light) when the axes of the two plates were crossed, whether the source of heat were a lamp or brass heated below luminosity. He also proved that heat, like light, is polarized in the pro- cesses of reflection and refraction. In his refraction ex- periments he employed mica split by heat, and therefore acting like a bundle of plates. In this state the substance, RADIANT HEAT. 179 ordinarily transparent, assumes a glossy silvery appearance, and, though nearly opaque to light, allows nevertheless a large portion of heat to pass ; and if the rays of heat make a proper angle with the surface they are found to be polar- ized to a considerable extent, and hence two such screens placed in opposite directions are found to stop a large portion of the incident heat. This result was found to hold for all kinds of heat, including that from the blackened sur- face of a vessel containing boiling water. In addition to these results Professor Forbes was able to prove the cir- cular polarization and depolarization of heat. Circular polarization was proved by using a rhomb of rock salt, while by interposing a film of mica between his polarizing and analyzing plates, which had their planes of incidence inclined at right angles to one another, and observing whether any difference of heating effect appeared when the principal section of the plate was parallel to the plane of primitive polarization or inclined 45 to it, he shewed the depolariza- tion of heat. Other observers have confirmed these results, and have furthermore shewn that very many of the phenomena of optics can be reproduced by dark heat. Indeed, the analogy between these two agents is as complete as our experiments are capable of shewing. Our instruments are doubtless very delicate, but it ought to be borne in mind that the most refined apparatus is far less sensitive for dark heat than the eye is for light. CONCLUDING REMARKS. 194. The facts detailed in this chapter all tend to shew that radiant light and heat are only varieties of the same physical agent, and also that when once the spectrum of a luminous object has been obtained, the separation of the different rays from one another is physically complete; so that if we take any region of the visible spectrum, its N 2 j8o REFLECTION, etc. OF RADIANT HEAT. illuminating and heating effect are caused by precisely the same rays. We may extend this observation to that region of the spectrum near the violet, or most refrangible extremity, which possesses not only a luminous but also a chemical effect, and assert that these two effects are caused by the same rays. The solar spectrum, it is well known, is inter- sected with dark lines, of which more hereafter; in the meantime suffice it to say that these lines have done good service in shewing that there is only one agent at one part of the spectrum. Thus towards the left extremity, or the red, we have at the same time a heating and a luminous effect. Now whenever a dark line occurs this of course denotes that a certain ray of light is absent, but by means of very delicate investigations with the thermo-pile it has been found that heat as well as light is absent from the spaces occupied by these lines. So also towards the right extremity, or violet, we have at the same time a luminous and a chemical effect, and we may therefore obtain a map of this region either from eye observations or by means of photography. Now when two maps obtained by these two different methods are com- pared together, it is found that the same dark lines occur in both, or, in other words, an absence of luminosity implies at the same time an absence of chemical effect. Furthermore, we have reason to suppose that the physical distinction between different parts of the spectrum is one of wave length, and that rays of great wave length are in general less refracted than those of small wave length. We would remark, in conclusion, that while the effects produced by different rays are generally divided into their heating, luminous, and chemical effects, yet there is a material distinction between the first of these and the other two. The luminous effect depends upon the constitu- tion of the eye, and may be possessed by certain rays and THEORY OF EXCHANGES. l8l by those alone ; the chemical effect also, as it depends upon the nature of the substance and of the change which it undergoes, may be possessed by certain rays but not by others. But we are led to think that the heating effect of a ray is the true physical measure of its power, so that by making (as we can make) any portion of the spectrum wholly available in heating a body and by esti- mating exactly the heating effect which is produced, we shall at once be able to know the amount of energy or vis viva of which this portion of the spectrum is possessed. CHAPTER III. Theory of Exchanges. 195. At an early stage in the history of radiant heat the following question arose. A hot body, we all know, radiates heat towards those bodies that are of a lower temperature than itself, but does it also radiate when sur- rounded by bodies of a temperature equal to its own or of a higher temperature ? In other words, is the radiation of a given body at a given temperature dependent upon the bodies that surround it, or is it independent of them ? Either hypothesis will serve to explain the fact that bodies of the same temperature neither gain nor lose heat by virtue of each other's presence, for we may either suppose that such bodies do not radiate at all to one another, or else that each one radiates and receives back as much heat as it gives out. Upwards of seventy years ago Professor Pierre Prevost, of Geneva, introduced this latter idea, and ever since that time it has been gaining ground, and is now very generally received. 1 82 THEORY OF EXCHANGES. Prevost's theory was called by its author that of a move- able equilibrium of temperature, and according to it bodies at all temperatures are constantly radiating heat to one another, while those of a constant temperature get back as much heat as they give out. The equilibrium suggested by Prevost is not therefore a statical or tensional equilibrium or one of repose, but it is essentially an equilibrium of action ; and viewed in this light it would seem to flow naturally from the dynamical hypothesis which views all heat as a species of motion. Let us take, for instance, a thermometer : this, according to the theory of exchanges, is constantly giving out heat at a rate depending on the temperature of the bulb and independent of that of the surrounding enclosure. On the other hand, it is receiving heat from this enclosure at a rate depending upon the temperature of the enclosure and independent of that of the bulb. Thus its heat ex- penditure depends upon its own temperature, its heat re- ceipts upon that of the enclosure, and there is equilibrium of temperature when its expenditure is exactly balanced by its receipts. 196. A curious experiment by Pictet was probably the means of leading Prevost to this theory. Pictet, reversing the experiment of Art. 186 (Fig. 39), put ice, or a freezing mixture, in the focus of one of the reflectors and a ther- mometer in that of the other. And in consequence of this the temperature of the thermometer was found to fall. This fall would be at once explained if we could suppose cold to be a principle susceptible of radiation. It was. probably his conviction of the inadmissibility of this explanation that led Prevost to frame the theory of exchanges, and a very little consideration will shew that this phenomenon can be easily explained by this hypothesis. Referring to Fig. 39, let us first take the case in which the bulb of the thermometer THEORY OF EXCHANGES. 183 at D is of the same temperature as the substance at A. According to the theory of exchanges, rays DE, DF, &c. will proceed from the bulb D, and ultimately, by virtue of the laws of reflection, will be concentrated upon the sub- stance at A. In order therefore that the bulb D may not lose heat, it is necessary that the place of these rays be supplied by other rays of equal intensity, that is, by AB, A C, &c. which proceed from A and ultimately fall upon D. It thus appears that when D and A are of the same temperature both sets of rays are of equal intensity, and hence the thermometer will remain stationary. Again, when A is warmer than D the rays which reach D from A are more intense than those which reach A from D, and hence D will gain heat, or the thermometer will rise ; this is the ordinary experiment. But, on the other hand, when A is colder than D the rays which leave D for A will be more intense than those which reach D from A, and hence D will be deprived of heat, or the thermometer will fall ; this is Pictet's experiment. We see therefore that the theory of a moveable equili- brium explains very well the apparent reflection of cold, and that according to this theory, the same cause which in the one case makes the thermometer peculiarly sensitive to an increase in the temperature of the opposite body (that is to say, the reflection from the concave mirrors), will in the other make it equally sensitive to a diminution of the same temperature. 197. Besides this happy explanation the hypothesis of Prevost has consistently vindicated its claims to represent the truth, not only by explaining very many experiments, but also by suggesting new truths which have afterwards received an experimental verification. This theory, since its proposal by Prevost, has been de- veloped by Provostaye and Desains, and more recently by 184 THEORY OF EXCHANGES. the author of this work and by Kirchhoff. It will, perhaps, best conduce to clear conception if we assume at first the truth of this hypothesis, then deduce its legitimate con- clusions, and shew at the same time that these are all supported by experiment. Deferring until next chapter a proof in favour of the theory derived from the laws of cooling as ascertained by Dulong and Petit, let us for our present purpose imagine to ourselves a chamber of the following kind. 198. Let the walls which surround this chamber be kept at a constant temperature, say 2 1 2 Fahr., and let them be covered with lamp-black a substance which reflects no heat, or at least very little ; also let there be a thermometer in the enclosure. It is well known that this thermometer will indicate the temperature of the surrounding walls, and that it will be a matter of indifference whether it be hung in the middle of the enclosure or at one of the sides ; in whatever part of the enclosure this instrument is placed its indication will be precisely the same, namely 212 Fahr. (In what follows it ought to be clearly borne in mind that we are now supposing the theory of exchanges to be true, according to which bodies even of the same temperature are always giving and receiving radiant heat.) EQUILIBRIUM OF HEAT-RAYS. 199. Heat equilibrium of surfaces. Suppose that the outside of the bulb of this thermometer is covered with tinfoil, so that its reflecting power is considerable. Now according to the theory of exchanges this thermometer is constantly radiating heat towards the lamp-black, but it is receiving back just as much as it radiates. Let us call the radiation of lamp- black 100, and suppose that 80 of these 100 rays which strike the thermometer are reflected back from its tinfoil surface, while the remaining 20 are absorbed. Since therefore the THEORY OF EXCHANGES. 185 thermometer is absorbing 20 rays, and since nevertheless its temperature is not rising, it is clear that it must also be radiating 20 rays, that is to say, under such circumstances its absorption and radiation must be equal to one another. If we now suppose the outside of the bulb to be blackened instead of being covered with tinfoil, the thermometer will absorb nearly all the i oo rays that fall upon it, and just as in the previous case, since its temperature is not rising, it must be radiating i oo rays. Thus we see that when covered with tinfoil it only radiated 20 rays, but when blackened it radiates 100. The radiation from a reflecting metallic surface ought therefore, if our theory be true, to be much less than from a blackened one. This has been proved experimentally by Leslie, who shewed that good reflectors of heat are bad radiators. 200. Again, we have seen that in the case of the bulb covered with tinfoil 80 of 'the 100 rays which fell upon it were reflected back, and we have also seen that 20 rays were radiated by the bulb. Hence the heat reflected plus the heat radiated by this thermometer in the imaginary enclosure will be equal to i oo, that is to say, it will be equal to the lamp- black radiation from the walls of the enclosure. We may generalise this statement by saying that in an enclosure of constant temperature the heat reflected plus the heat radiated by any substance will be equal to the total lamp-black radi- ation of that temperature, and this will be the case, whether the reflecting substance be placed inside the enclosure or whether it form a part of the walls of the enclosure. In fact, we may conceive the walls of such an enclosure to be formed of a large variety of substances from polished metal to lamp- black, and yet the total flow of radiant heat coming from one portion will be the same as that coming from another portion, the only difference being that in the case of a re- flector, such as the thermometer with tinfoil, this heat is 1 86 THEORY OF EXCHANGES. partly radiated and partly reflected, while in the case of lamp- black it is altogether radiated, the reflection being insensible. The statement that the heat reflected plus the heat radiated by any substance in an enclosure of constant temperature will be equal to the total lamp-black radiation of that tempe- rature has been experimentally verified by MM. Provostaye and Desains, who found Radiation from polished silver at a given temp. = 2.2 Reflection by silver of rays from lamp-black at this temperature represented by i oo = 97.0 Sum = 99.2 Now 99.2 comes very near the lamp-black radiation or TOO. They also found that the sum of the reflected and radiated heat from glass at different angles was equal to 93.9 (lamp- black radiation being equal to 100); the difference between 93.9 and TOO they supposed to be due to diffuse reflection. 2O1. Let us now once more return to our chamber of constant temperature, and imagine the thermometer carried from one part of the chamber to another where the surface is of a different shape. We may, for instance, pass from Fig. 43, where the ther- mometer T is at the centre of a sphere, to Fig. 44, where it is within an acute angle. In the first case, the rays which reach the instrument will be those whichhavebeen emitted Fig. 43. Fig. 44. by the surrounding spherical envelope in a direction perpendicular to the surface; but in the latter case, most of the rays reaching the thermometer will have been THEORY OF EXCHANGES. 1 87 emitted in an oblique direction. Yet the thermometer receives precisely the same amount of heat in both cases, and will always do so, whatever be the shape of the surrounding enclosure. In fine, in such an enclosure streams of heat may be supposed to be passing and repassing in every possible direction, and to be equally intense in all directions, without the least regard to the shape or substance of that part of the enclosure from which they come. Thus the stream of radiant heat impinging upon the surface AB (Fig. 45) in the direction CA perpendicular to A B will be the same whether it be supposed to proceed from a surface CD parallel to A B or from a surface CE inclined to A B. It thus appears that in our hypothetical enclosure of Fl S- 45- constant temperature the heating effect of a stream of heat is solely dependent upon its cross section, that is to say, upon the extent of surface AB perpendicular to its direction which it will exactly cover. This result has been verified experimentally by Provostaye and Desains ; these observers having found, as we have already said, that the sum of the reflected and radiated heat from glass at different angles is a constant quantity. When the source of the rays is a non-reflecting substance such as lamp-black, the statement of this law is very simple. We see from Fig. 45 that the heat which leaves the surface CD in the direction CA is precisely equal to that which leaves the surface CE in the same direction. Hence the heat which radiates from a surface of lamp-black in any direction is proportional to and may be represented by the projection of this surface upon a plane perpendicular to the direction of the rays. This result has been experimentally proved by Lambert 1 88 THEORY OF EXCHANGES. of Berlin and also by Leslie, who made observations upon the heat from blackened surfaces at different angles. The method of observation is very simple. Fig.. 46 _\ P* ^^^^^^L XAMXJUJiA B' A . B - Ptlt Fig. 46. represents the arrangement, where A is an aperture behind which the heated body is placed. Now if this body be a black- ened surface, it is quite immaterial whether it be placed in the position B or ', provided it be large enough to fill up, in the latter position, the field of view from the cone ; in both cases the galvanometer attached to the pile will give the same indication. Undoubtedly, when the surface is in the position ', a greater extent of this will be viewed by the cone; but as far as radiant heat is concerned, we may imagine the surface to be projected upon the aperture A, so that if the field behind this aperture be filled up by the blackened surface its inclination or curvature is of no consequence. 202. We have seen that the stream of radiant heat which beats upon the thermometer in our enclosure of constant temperature is independent both of the materials and of the shape of -the walls of the enclosure, so that if the instrument be carried from one part to another, there will be no change in the amount of radiant heat falling upon it. Something more however is necessary, for we must not only have the quantity of heat which falls upon the thermometer the same throughout, but the quality of this heat must also THEORY OF EXCHANGES. 189 remain the same. It will be necessary to give a short ex- planation of the word ' quality' It is well known that different kinds or qualities of light affect the same substance in different ways, thus red glass will absorb green light while it will allow red light to pass. In like manner there are a great many different kinds of dark heat, and the same substance will absorb some of these much more rapidly than others. So also heat as well as light may be polarized, and we have already seen (Art. 193) that a substance such as tourma- line absorbs heat polarized in one plane with greater avidity than heat polarized in a plane perpendicular to the former. Now the word 'quality' is here taken to denote any difference^ whether of ivave length or polarization., which causes rays of heat to be differently absorbed by any substance. When we say therefore that two pencils of heat. are of the same quality, we mean that the mixture of wave lengths, in the one is precisely the same as in the other, and also that the polarization of both is the same. Suppose now that our thermometer is covered with some substance which displays this selective absorption for certain kinds of heat, and that we carry it about from one part of the enclosure to another. It will not only be necessary that the quantity of radiant heat which beats upon our thermometer shall be the same throughout the enclosure, in order that the instrument may preserve its constancy of temperature, but the quality of this heat must also be the same ; for if not, we might suppose that in one place the heat is of a kind that is greedily absorbed by the coating of the bulb, and that in another place it is of a kind that is reflected back from this coating; thus although the quantity of heat falling on the bulb might be the same in both places, yet the thermometer would absorb more in the first case than in the second, and its constancy of temperature would be destroyed. It is therefore clearly necessary that the stream of radiant heat 190 THEORY OF EXCHANGES. which beats against the thermometer as it is carried about in the enclosure should be the same at all places, both as regards quantity and quality. Various experiments go to prove this uniformity both in the quantity and quality of the heat from different parts of an enclosure of constant temperature. Perhaps the most striking of these is that when an enclosure is heated to a red or white heat the luminous rays from the different parts of this enclosure will be the same both in quantity or luminosity, and in quality, or colour, and will depend only on the temperature, and not on the nature of the materials composing the walls of the enclosure. Again, as regards polarization, certain experiments by Provostaye and Desains appear to shew that the stream of heat in an enclosure of constant temperature is unpolarized, and that if there be a reflecting substance in the enclosure, so that the reflected portion of the heat from it is polarized, then the radiated heat from this substance will be polarized in the opposite way, so that the whole heat reflected and radiated together is unpolarized. 203. We are now in a position to extend the remark already made (Art. 199) with regard to the equality of the absorption and radiation of a surface in our hypothetical enclosure. Such a surface must not only give back by radiation to the general stream of heat as much as it with- draws by absorption, but what it gives back must be of the same quality as that which it withdraws. The absorption of such a surface will therefore be equal to its radiation, and this equality will hold for every individual kind of heat of which the whole heterogeneous radiation is composed. 204. We deduce therefore, as the result of our inquiries, both theoretical and experimental, in this branch of our subject, that in an enclosure of constant temperature i. The stream of radiant heat is the same throughout, THEORY OF EXCHANGES. 19! both in quantify and qualify ; and while it depends on the temperature it is entirely independent of the materials or shape of the enclosure. 2. This stream is unpolarised. 3. The absorption of a surface in such an enclosure is equal to its radiation, and this holds for every kind of heat. 205. Heat equilibrium of plates. Returning once more to our chamber of constant temperature, let us sus- pend in it a thin plate of rock salt. Now since the tem- perature of this plate remains constant, the plate must radiate just as much heat as it absorbs. But rock salt (Art. 191) absorbs very little heat, hence also it will radiate very little. Moreover, a thick plate will absorb more than a thin one, and hence also it will radiate more. Both of these con- clusions have been verified by the author of this work. By making use of the thermo-pile he has found that the radiation from a thin plate of rock salt is only 15 per cent, of the total lamp-black radiation for the same temperature, and that the radiation from a thick plate of rock salt is greater than from a thin one. 206. Suppose, however, that instead of rock salt we had suspended two plates of glass of unequal thickness. Since this substance is extremely athermanous, either of these plates would probably absorb nearly all the heat which fell upon it, and hence the radiation of both plates (radiation being equal to absorption) would be sensibly the same, and would be very great in fact it would be much the same as if they stopped the whole heat, or were covered with lamp-black. 207. From this we see what it was that misled the early experimentalists on this subject, and induced them to think that radiation was confined, if not to the surface of a body, at least to a very small depth beneath it. They found that 192 THEORY OF EXCHANGES. when a metallic surface was coated with varnish its radiative power was very much increased, but that very soon this increase attained its maximum, after which an additional coating produced no further effect. But the reason of this was, not that radiation is in all cases confined to a very small distance beneath the surface, but that these coatings were of a very athermanous substance, so that a very small thickness was practically equivalent to a surface of lamp- black. Could it have been possible to apply a coating of transparent rock salt, the result would have been very dif- ferent. 208. Let us now take our thermometer and cover its bulb once more with a substance having a selective absorp- tion for heat, and, further, let us hang up before it in the enclosure a plate of rock salt. No change in its indication will take place; but in order that the temperature of this thermometer may remain without change it is obviously necessary that this plate of rock salt should change neither in quantity nor in quality the stream of heat which impinges against the bulb; that is to say, this stream after it has passed through the salt must be precisely the same both in quantity and in quality as before it entered it. In order that this may be the case it is necessary that the absorption of the rock salt should be equal to its radiation for every kind of heat. This result has also been verified experimentally by the author of 'this work. If the kind of heat which rock salt radiates be the same as that which it absorbs, it would follow that a cold plate of rock salt ought to be exceedingly opaque to the radiation from heated rock salt. This was found to be the case. A moderately thick plate of this substance was found to stop at least three-fourths of the heat from a thin plate of heated rock salt, whereas it will only stop a small proportion of ordinary heat. THEORY OF EXCHANGES. 193 209. This affords an explanation of the fact that two plates of rock salt placed the one behind the other, or a single plate of double thickness, do not radiate twice as much as a single plate. For let EF A be the front surface of such a double plate, of which CD represents a line mid- way between the two surfaces. Now, while as much heat will cross the line CD from the hinder half of the plate as would be radiated from the single plate ABCD, a great proportion of this heat (probably three-fourths) will be absorbed by the front half in its passage through it, since we have seen that rock salt absorbs intensely the heat which it radiates. Hence, if the radiation of the single plate be = i, that, of the double plate, instead of 2, will probably not be more than ij. 210. Our readers will thus be prepared to see that ra- diation is a thing which goes on in the interior of a plate just as much as near the surface; and they will also see that it does not necessarily follow from this that the radia- tion of a plate should be proportional to its thickness, but very much the reverse ; indeed, had the substance of the plate in Fig. 47 been glass instead of rock salt, the single plate would have given out sensibly the same amount of heat as the double plate, since in the latter the heat from ABCD would all have been stopped by CDEF. We are thus prepared to see that in the interior of substances, as well as in air or vacuo, a stream of radiant heat is constantly passing and repassing in all directions, and in the case of constant temperature, as this stream of heat passes any layer of particles it is just as much diminished by the absorbing action of these particles as it is recruited by their radiation, so that the stream flows on virtually unchanged o 194 THEORY OF EXCHANGES. both in quantity and quality until at last it reaches the surface. 211. Amount of internal radiation. We have now to consider a more difficult question, which may be thus stated. Supposing we have several different substances all remaining at the same constant temperature, will the streams of radiant heat continually passing and repassing in the interior of these substances be equal to each other ? In the first place, and before attempting to answer this question, we must shew how the intensity of a stream of radiant heat may best be measured. For this purpose let us suppose a small square surface representing unity of area to be placed in the interior of an enclosure, or of a substance surrounded by an enclosure kept at an uniform temperature. In accordance with our views, streams of radiant heat will be continually passing through this surface in all directions ; let us confine our attention to these rays, which are as nearly as possible perpendicular to the plane of our square unit. But it may be said, why not confine our attention to rays strictly perpendicular to this plane ? In answer to this, we remark that in our present investigation (the reason will afterwards appear) we must regard a ray in the sense in which a straight line is regarded. And just as a line is in reality always part of the boundary of a solid, so a ray is always in reality part of the boundary of a beam or pencil of light. We may satisfy ourselves that this is the case in nature by considering the light which reaches the eye .from a star or other object apparently very small; this would seem to be the nearest approach to a geometrical line of light, whereas since a star has a certain real though very minute angular diameter, the light from it is in reality a converging pencil, although no doubt the angle of convergence is very small. We will confine our attention therefore to rays as nearly THEORY OF EXCHANGES. 195 as possible perpendicular to our unit area. Let B (Fig. 48) represent this area, and let CBD be a very small pencil or cone of rays nearly perpen- dicular to the plane of B, the central line AB being strictly perpendicular to this plane. Now if we suppose the angle CBD as well as our unit area to remain constant while we pass from one substance to another, then the quantity of heat radiated in unit of time upon this unit area B through directions comprised within the small cone CBD will denote the intensity of internal radiation of the substance in question. \ 212. The circle CAD may in fact be com- LB J pared to the disk of a small star whose diameter p . g CD subtends with the eye the angle CBD (greatly exaggerated in the diagram for the purpose of demonstration), and from which a beam or pencil of light represented by the cone CBD reaches the eye of the ter- restrial observer at B. Now imagine, for the sake of demon- stration, that it is possible to place the eye in the interior of a substance of constant temperature, and also that the eye is sensible to all the rays which compose, according to our hypothesis, the entire radiation of the substance, then it is evident that if the eye look in the direction of CAD, the brightness of the field of view in front of the eye or of any given detached portion of it, such as the area CAD, will indicate the internal radiation; so that, if the eye be now removed to the interior of another substance of greater internal radiation, more rays will strike it in front from CA D in one second of time, and the field of view will therefore appear brighter in the very same proportion in which the internal radiation is increased. 213. Let us now direct our attention to an enclosure, such as a sphere (Fig. 49), kept at a uniform temperature, O 2 196 THEORY OF EXCHANGES. and suppose the lower half of this enclosure to be filled with an uncrystallized solid or liquid (index of refrac- tion = /*) while the upper half is a vacuum. Let us also suppose that the external boundary of this upper half of the sphere is covered with lamp-black, and let the area B be now placed on the sur- face of the solid or liquid, while the area CAD is a very small circle approxi- mately coinciding with the Fig. 49. lamp-black boundary of the sphere. Let us denote by R the radiation of lamp-black, that is to say, R will repre- sent the number of heat rays which reach the unit area B through the directions of the cone CBD in one second of time. 214. Part of these rays reaching B will be reflected back ; let us call this reflected portion a R ; then R a R, or (i a) R, will denote the amount of these rays which really penetrate the medium in one second of time. But these rays will be bent by refraction towards the perpendicular, after entering the medium, and will therefore be comprised in a cone C'BD' with a smaller angle than CBD. The angle C'BD' may very easily be found ; for sin CBA sin C'BA ~ F ' or, since these angles are very small, CBA CBD = u or ~ M /"" Z? A ' ' ' /"" 7? TV C J3 A C -fj JLJ We thus see that of the rays under consideration a portion THEORY OF EXCHANGES. 197 equal to (i a) R enters the substance, and is after its entrance embraced in a cone of which the angle 215. But since the substance we are considering, being of constant temperature, gains as much heat as it loses in all of its parts, it follows that as much heat must pass out by B along lines embraced within the cone C'BD' as passes into the substance through these same directions. Hence the quantity of heat which will pass out of the substance by B along lines embraced within a cone having the angle C'BD' will (for one second of time) be (i a) R. 216. Now let R' be the unknown internal radiation for the medium; that is to say, let R' denote the quantity of heat rays which will in one second reach B from the interior in directions comprised within a cone which has a constant standard angle equal to CBD (Art. 211). We must find what fraction of this radiation will reach B if the angle be C'BD' instead of CBD. It is evident that the amount of heat reaching B through the directions of the cone CBD will be proportional to the area CAD, and this area will be proportional to the square of CD, and very nearly to the square of the angle CBD. Hence Heat through CBD' : heat through CBD ( = #') : : (C'BD'? : (CBDf. Therefore /C'BD'\ R' Heat from interior through C'BD' = R' x ( ---- J = -^ by Art. 214. r>' We thus see that a quantity of heat = $ will in one second of time reach B from the interior through the cone C'BD'. But of this heat we know from the laws of optics that the amount a ( -J will be reflected back into the 198 THEORY OF EXCHANGES. r>' interior, and hence (i a) T will be the heat which passes out through B through the cone C'BD'. 217. We have thus obtained two expressions, one for the heat which enters the substance through B and diverges through the directions of the cone C ' B D ', namely (i a) R (Art. 214), and the other for the heat which passes out through 7?' B through the same cone, namely (i a) ^ ; and we have seen (Art. 215) that these two expressions must be equal to one another. Hence (i a) R = (i a) - z ', That is to say, the internal radiation in a substance of which the index of refraction is p will be n 2 R, R denoting the radiation of lamp-black corresponding to the temperature of the experiment. It is also clear from what we have said that this relation will hold for every individual description of heat of which the whole radiation is composed. EQUILIBRIUM OF LIGHT RAYS. 218. It is of importance to extend these observations to radiant light, or to those rays which affect the eye, and this extension has been made both by Professor KirchhofF of Heidelberg and by the author of this work. We have already endeavoured to accumulate evidence in favour of the opinion that radiant light and heat are only varieties of the same physical agent, differing from one an- other simply in wave length; but during the progress of this branch of science many inquirers have been inclined THEORY OF EXCHANGES. 199 to think that light and heat are physically distinct, although possessing many properties in common, and it has even been imagined that some kinds of light are entirely destitute of any heating effect. But if it can be shewn that the consequences of Prevost's theory extend to radiant light, we are furnished with very strong evidence in favour of that hypothesis which regards heat and light as varieties of the same agent. 219. Prevost's theory consists of the three following statements. 1. If an enclosure be kept at a uniform temperature, any substance surrounded by it on all sides will ultimately attain that temperature. 2. All bodies are constantly giving out radiant heat, at a rate depending upon their substance and temperature, but independent of the substance or temperature of the bodies that surround them. 3. Consequently when a body is kept at uniform tempe- rature it receives back just as much heat as it gives out. From these statements follow all the laws that have been deduced for radiant heat. But in the process of argument it is essential to regard the rays under consideration as being capable of heating the bodies on which they fall and by which they are absorbed. Hence, if this theory extend to light, it follows that uminiferous rays are capable also of heating more or less the bodies by which they are absorbed. The following experiments exhibit the extension of the theory of exchanges to rays of light. 220. Light equilibrium of surfaces. It has been shewn with respect to Heat (Art. 199) that good reflectors are bad radiators, and a similar experiment may be made for light. Thus if a pot of red-hot lead or tin be carried into a dark place and the dross scummed aside by a red-hot 2OO THEORY OF EXCHANGES. iron ladle, the liquid metal will appear less luminous than the surrounding dross. Also if a piece of platinum partly polished and partly tarnished be held above the flame of a Bunsen's burner in a dark room, the tarnished portion will shine much more brilliantly than the polished. Finally, if we take a piece of stoneware of a black and white pattern, heat it to redness and then view it in the dark, the black will shine much more brightly than the white, presenting a very curious reversal of the pattern, which we have endeavoured to delineate in Figures 50 and 51. Fig. 50- Fig- 5*- 221. Light equilibrium of thin plates. Experi- ment I. If a piece of colourless transparent glass be heated to redness in the fire, removed to the dark, and then viewed, it will be found to give out very little light ; but if the glass be coloured, its light radiation will be more copious, the amount of light given out depending upon the depth of colour. This is an experiment analogous to that with rock salt, and it is evident that colourless glass gives out but little light because it absorbs .but little. A stratum of heated air THEORY OF EXCHANGES. 2OI may likewise be instanced as a substance which neither absorbs nor emits light or heat to a sensible degree. 222. Experiment IL It has been shewn that the heat radiated by a thin plate of any substance at a given temperature is precisely that kind of heat which the plate absorbs when heat of that temperature is allowed to fall upon it. Now the same thing holds with regard to light. With respect to the rays proceeding from an or- dinary fire, all coloured glasses may be divided into two groups, those which redden and those which whiten the fire as we look through them. The first group comprises red and orange glasses, and these absorb the whiter de- scriptions of light ; the second group comprises green and blue glasses, and these absorb the redder kinds of light. We should therefore expect red and orange glasses to give out, when heated, a peculiarly white light, and green and blue glasses a peculiarly red light. Now this is found to be the case. A red glass coloured by gold, when heated to redness, removed, and viewed in the dark, gives out a milky-white or even greenish light, and the orange glasses used by photographers do the same. On the other hand, green and blue glasses give out, when thus heated, a red- dish kind of light. This experiment is analogous to that wherein it is shewn that a cold plate of rock salt stops a large proportion of the heat from a hot plate of the same substance. 223. Experiment III. Again, we know (Art. 193) that when a ray of ordinary light falls upon a plate of tour- maline cut parallel to the axis, it absorbs nearly all that resolved portion of the rays which is polarized in a plane parallel to the axis of the crystal, while it allows to pass a considerable portion of those which are polarized in a plane perpendicular to the axis. Now it can be shewn that if such a plate be heated red hot, the rays of light 202 THEORY OF EXCHANGES. which it gives out are partially polarized in the same di- rection as those which it absorbs, viz. in a plane parallel to the axis. This experiment may best be tried by a method devised by Professor Stokes, in which a hollow cast-iron bomb is heated to redness. This bomb is re- presented in Figures 52 and 53. In Figure 52 we see it Fi g- 52. Fig. 53. as it appears from the outside, with a small hole by which we can see through it. Fig. 53 represents a cross cut through the centre of the bomb, shewing the tourmaline T attached to a stand, C denoting the moveable lid. This tourmaline is in the very centre of the bomb, and hence in looking through the bomb, by means of the small hole, the eye encounters the plate of tourmaline. Now let this bomb be heated to redness, having the tourmaline inside of it, and then taken out of the fire and placed in the dark. The tourmaline will cool very slowly in this position, since it is (with the exception of the small hole) entirely surrounded by a red-hot enclosure, viz. the interior of the bomb, which, if the iron be sufficiently thick, will remain hot for some time. Now the eye in looking through the bomb by means of the small hole will encounter the radiated light from the heated tourmaline, and by means of a polari- scope it is easy to ascertain in what plane this light is THEORY OF EXCHANGES. 203 polarized. It will be found to be polarized in a plane at right angles to that in which light is polarized as it passes through the same tourmaline when cold and similarly placed. 224. Experiment IV. We have seen that in an enclosure of uniform temperature the flow of radiant heat is the same in all directions, both as regards quantity and quality, whatever be the substances with which the enclosure is filled. Now with regard to light a good coal fire may be viewed as an enclosure of approximately uniform tem- perature, and accordingly we ought to find that, whatever substances be put into this fire, when these ultimately become of the same temperature as the fire, they will not alter the nature of the light which is given out. We may prove this by throwing coloured glasses into the fire, and when these become sufficiently heated they will be found to have lost all their colour. The red glass, for instance, which we have thrown in will, as we have already seen, give out a greenish light on its own account; but it will pass red light from the coals behind it in such a manner that the light which it radiates precisely makes up for that which it absorbs ; so that we have virtually a coal radiation coming partly from and partly through the glass. 225. We cannot conclude this subject without alluding to a very interesting experiment first made by Foucault, but afterwards revived and extended by Kirchhoff, in which the .equality between radiation and absorption is extended to individual rays of the spectrum. Foucault found that the voltaic arc formed between char- coal points often emits the ray D of the solar spectrum on its own account, and at the same time absorbs it when it comes from another quarter. Kirchhoff, again, found that coloured flames, in the spectra of which bright sharp lines present themselves, weaken rays of the colour of these lines when such rays pass through the flames. We thus 204 THEORY OF EXCHANGES. see that the same media which in a heated state emit rays of a certain refrangibility in great abundance have also the power of stopping these rays when they fall upon them from another source. CONCLUDING REMARKS. 226. We have thus arrived both theoretically and ex- perimentally at a law which may be enunciated as follows : Bodies when cold absorb the same rays which they give out when hot. The reader will at once be struck with an analogy between sound and light in this respect. A musical string when at rest takes to itself and therefore absorbs the very note (given out by another instrument) which it will itself give out when in a state of vibration. Reasoning from this analogy Professor Stokes had sug- gested beforehand the probability of a connexion between the absorption and radiation of bodies for particular rays of the spectrum, and he also imagined that this suggestion would account for the dark lines in the solar spectrum. The prediction of this philosopher has been abundantly confirmed by the labours of KirchhofT; but the striking con- clusions with regard to the constitution of the sun and stars which Kirchhoff has experimentally arrived at must be de- ferred till another chapter. We cannot, however, refrain from remarking that the law developed in this chapter affords a valuable confirmation by analogy of the truth of the undulatory theory of light. The likeness between a vibrating string and a heated particle has been remarked above, and we have seen that a particle (just as a string with regard to sound) absorbs the same kind of ray which it gives out. It is, perhaps, allowable to infer that light, like sound, consists of undulations which are pro- pagated in a medium surrounding bodies, and that when heat or light is absorbed by a particle, the motion is con- RADIATION AT DIFFERENT TEMPERATURES. 205 veyed from the medium to the particle, just as when a string takes up a note passing through the air the motion is conveyed from the air to the string ; and that, again, when heat or light is radiated by a particle it is similar to the giving out by a string of its note to the air.. CHAPTER IV. Radiation at Different Temperatures, 227. It has already been shewn (Art. 204) that the stream of radiant heat continually proceeding through an enclosure of which the walls are kept at a constant temperature depends only on the temperature of the walls, and not on the nature of the various substances of which they are com- posed ; the only difference being that for metals this stream is composed partly of radiated and partly also of reflected heat, while for lamp-black it is composed wholly of radiated heat. This may be expressed by saying that this stream depends upon or is a function of the temperature, and of it alone; but there is the following very important difference between a reflecting and a lamp-black surface, as repre- senting this stream of radiant heat. It is only when a reflecting surface forms part of a com- plete enclosure of the same temperature as itself, that the radiated and reflected heat from this surface together repre- sent the whole stream of heat; for if we bring it for a moment into another enclosure of lower temperature, the reflected heat is altered, and although the radiation will for a short time continue nearly constant, yet this radiation will not represent the whole stream of heat due to the tempera- ture of the surface. 2O6 RADIATION AT On the other hand, if a lamp-black surface be placed in the above position, since the stream of heat which flows from it is entirely independent of the reflection due to neighbouring bodies, the heat which it radiates when brought for a moment into an enclosure of lower temperature than itself will truly represent the stream of radiant heat due to the temperature of the lamp-black. 228. Suppose now that we have a thermometer with a blackened bulb, and that this is placed in a blackened enclosure of a lower temperature than itself, the heat which it radiates will represent the total radiation due to the tem- perature of the bulb, while that which it receives will repre- sent the total radiation due to the temperature of the enclosure, and the difference between these two will thus be represented by the loss of heat experienced by the ther- mometer. Thus, if 6 be the temperature of the enclosure, and / + that of the bulb, then, since the stream of radiant heat (Art. 204) is a function of the temperature only, we shall have this stream represented by F(t+6} and F(6) for these two temperatures, and the rate at which the thermometer loses heat will be denoted by F(t+6)-F(6). This is the rate at which the instrument loses radiant heal, and it will also represent the rate at which it loses temperature, or the velocity of cooling, as this is termed, if we suppose that the specific heat (or heat required to pro- duce a change of i) of the mercury of the thermometer remains the same for all the temperatures of the experiment. This, though not precisely, is very nearly the case, and hence the velocity of cooling of a thermometer placed in these circumstances may be regarded as representing with great accuracy the intensity of radiation. With these remarks we shall now discuss the experiments that have been made on velocity of cooling. DIFFERENT TEMPERATURES. 2OJ VELOCITY OF COOLING ; VARIATION WITH TEMPERATURE OF QUANTITY OF RADIATION. 229. Newton was the first to enunciate his views on the cooling of bodies. He supposed that a heated body ex- posed to a certain cooling cause would lose at each instant a quantity of heat proportional to the excess of its tempera- ture above that of the surrounding air. It was, however, soon found that this law was not exactly followed, and several philosophers made experiments on the subject with more or less success, until the time of MM. Dulong and Petit, who made a very complete and successful investigation of the velocity of cooling of a thermometer both in vacuo and in air. It is with their experiments in vacuo that we have now to do. 230. The apparatus used by these experimentalists con- sisted of a hollow globe of thin copper with the interior blackened, which could be immersed in a vessel of water of known temperature. Through an orifice in this globe a thermometer could be inserted, so as to have its bulb in the centre of the globe. The temperature of this thermo- meter was always higher than that of the globe, and the number of degrees that the mercury would sink in a minute, supposing the cooling to be uniform during that time, was taken to denote the velocity of cooling. A preliminary set of experiments was first made, from which it appeared that the law of cooling of a liquid mass is independent of the nature of the liquid and of the form and size of the vessel which contains it. Having determined this, MM. Dulong and Petit proceeded to make their final experi- ments with a thermometer containing about 3 Ibs. of mer- cury. In the first instance this thermometer preserved its natural vitreous surface, but since glass is exceedingly opaque towards the heat radiated at all the temperatures of the 208 RADIATION AT experiment, the results may be regarded as being nearly identical with those which a thermometer with a blackened bulb would have given. The following were the results obtained where the tem- perature of the enclosure was that of melting ice. Excess of temperature of the thermometer. 240 220 200 180 160 140 120 100 Velocity of cooling. C. 10.69 8.8 1 7.40 6.10 4.89 3.88 3.02 2.30 1.74 We see at once from this table that the law of Newton does not hold, for according to it the velocity of cooling for an excess of 200 should be precisely double of that for an excess of 100: now we find that it is more than three times as much. 231. In Dulong and Petit' s experiments both the excess of temperature of the thermometer and also the absolute temperature of the enclosure were made to vary, that is to say, both / and 6 varied; and they obtained the following results. Excess of temperature of thermometer. Velocity of cooling, for various temperatures of enclosure. (') = oC. 0=20C. = 40C. = 6oC. = 8oC. 240 10.69 I2.4O 14-35 ... 220 8.81 10.41 11.98 ... 2OO 7.40 8. 5 8 IO.OI 11.64 ^'45 180 6.10 7.04 8.20 9-55 11.05 160 4.89 5-67 6.6 1 7.68 8-95 140 3.88 4-57 5-32 6.14 7.19 120 3.02 3.56 4-15 4.84 5-64 100 2.30 2.74 3-i6 3.68 4.29 80 1.74 1.99 2.30 2-73 3.18 60 1.40 1.62 1.88 2.17 DIFFERENT TEMPERATURES. 309 Now if we divide the numbers of the third column by the corresponding numbers of the second for instance, 12.40 by 10.69 we find the quotient to be 1.16; and con- tinuing the process for the other numbers in these columns, we find : 3rd column - gives as quotients, i.io. 1.18. i.io, 1.15, 2nd column G 1.16, 1.17, 1.17, 1.18, 1.15. In like manner 4th column 3rd column 1.17, 1.16, 1.17, 1.15, 1.16, 1.16. 5th column gives as quotients, 1.16, 1.15, 1.16, 1.16, .15, 1.16, 1.16. gives as quotients, 1.15, 1.16, 1.16, 1.15, 4th column 1.17, 1.16, 1.18, 1.16. 6th column 5 th column giveS a qu tients ' '' I5 ' .* w * ''** 1.16, 1.17, 1.17, 1.15. These numbers are all nearly the same, and their mean is 1.165. Hence we see that corresponding numbers in the various columns form a geometrical progression, so that if we denote a number in the second column by unity we shall have i, 1.165, (i.i65) 2 , (i.i65) 8 , (1.165)*, as representing the velocities of cooling for the same excess of temperature for the cases where the temperature of the enclosure is denoted by o, 20, 40, 60, and 80. We are thus entitled to say that the velocity of cooling of a thermometer in vacuo for a constant excess of temperature increases in a geometrical progression when the temperature of the surrounding medium increases in an arithmetical progression, and the ratio of this progression is the same whatever be the excess of temperature. p 310 RADIATION AT 232. MM. Dulong and Petit soon saw that this remark would enable them to find the law of cooling. In the first place, it ought to be observed that the results already given are in accordance with the theory of exchanges, and that they form an additional proof of the truth of that theory. The theory of exchanges asserts that the loss of heat experienced by a thermometer cooling in vacuo is represented by the difference between the radiation due to the temperature of the thermometer and that due to the tem- perature of the enclosure. Hence, according to this theory, if A, B, C denote the absolute radiation at the temperatures a, b, c, of which a is the highest and c the lowest, then A B will represent the rate of cooling of a ther- mometer of temperature a in an enclosure of temperature b : BC will represent the rate of cooling of a ther- mometer of temperature b in an enclosure of temperature c : A C, or (A B) + (B C), that is to say, the sum of the two preceding rates will represent the rate of cooling of a thermometer of temperature (a) in an enclosure of temperature (c] if Prevosfs theory is true. Testing this by the table of Art. 231, we find that if a = 140 and b = 80 (/= 60, 6 = 80), then the velocity of cooling is 2.17. Again, if b = 80 and c = 20 (/= 60, 6 = 20), the velocity of cooling is found to be 1.40. Hence the sum of these two rates will be 2.17 + 1.40 = 3.57. Once more : if a = 140 and c = 20 (/= 120, B = 20), we find from the same table that the velocity of cooling is 3.56. Now this is as nearly as possible equal to the sum of the two preceding rates, which was 3.57 ; so that the DIFFERENT TEMPERATURES. 211 evidence derived from these experiments is decidedly in favour of the theory of exchanges. Assuming therefore the truth of this theory, MM. Dulong and Petit supposed that the velocity of cooling of a ther- mometer in vacuo may be represented by the function jry+ff^f'^ where the first term represents the absolute radiation of the thermometer whose temperature is /+#, and the second term the counter-radiation of the enclosure whose temperature is 0. 233. Now we have seen (Art. 231) that for an excess of temperature of 200 of the thermometer above that of the enclosure the velocity of cooling may be denoted thus Temperature of enclosure =OC. 20 40 Velocity of cooling (^=200) = 7.40 7.40(1.165) 7.40(1. 165)2 = 7.40 7. 4 o(i.oo77) 20 7.40(1.0077)* 7.40(1.0077)*. In like manner if /, or excess of temperature, = 180, we shall have Temperature of enclosure =oC. 20 40 6 Velocity of cooling (*= 1 80) = 6. 10 6.io(i.oo77) 20 6.io(i.oo77) 40 6.10(1.0077)^. It thus appears that for an excess = 200 we have 7.40 as a constant multiplier of the various terms, while for an excess = 180 this multiplier becomes 6.10. This multiplier varies therefore with the excess of temperature, or /, but not with the absolute temperature of the enclosure, or 0, if only the excess remains constant ; it is therefore a function of /, and we may represent it by $ (/), according to the usual notation. Hence we see that the velocity of cooling for any values of / and 6 may be represented by <#>(/) x (1.0077)'. But the velocity of cooling (Art. 232) is also represented by F(t+6)-F(0). Hence these two expressions must be equal to each other, or -F(6} = <(/) x (1.0077)'. P 2 212 RADIATION AT Dividing by (1.0077)0 we have F(t+i)-F(IF) (i.77) and expanding in terms of / we find , ** " (1.0077)9 dO (1.0077)0 d& 1.2(1.0077; Now since this equation must hold good for all values of / we may equate corresponding coefficients ; and hence ,; * 7 ^ = B = a constant quantity, d& (1.0077)0 Hence integrating Tt F(&] = w (1.007 7)0 + a constant quantity I if = w); and hence also F(t+6} = w(i.oo77)' + + a constant quantity. The velocity of cooling of the thermometer in vacuo will therefore be represented by where t+6 is the temperature of the thermometer, and 6 that of the enclosure in Centigrade degrees. The value of m in the present case is 2.037, as may be easily found from the table of results. When the bulb of the thermometer was covered with silver it was found that the velocity of cooling might be expressed by the same formula, only with a change in the value of m. Here it was necessary to suppose m = 0.357. 234. We are thus induced to suppose that the expression w (1.007 7) fl + a constant quantity, in which m varies from DIFFERENT TEMPERATURES. 213 one substance to another, will represent the absolute radia- tion corresponding to the temperature 6; but ihis expression must nevertheless be considered as an empirical formula satisfying observation, but which we are unable to deduce as a consequence from any known properties of matter. In truth our knowledge of the forces concerned in radiation is very small. MM. Prevostaye and Desains have since made experi- ments on the cooling of bodies, which tend to confirm the accuracy of the results obtained by Dulong and Petit. 235. Absolute measure of radiation. While the ex- periments of Dulong and Petit were admirably adapted to give the law of cooling, they are not so well fitted to de- termine in absolute measure the radiation from a heated body. This has since been done approximately by Mr.Wm. Hopkins. Mr. Hopkins represents by unity the quantity of heat required to raise 1000 grains of water one degree Centi- grade, and in terms of this unit he measures .R, or the amount of radiant heat, which would emanate in one minute from a square foot of a given surface. He thus obtained as the radia- tion in vacuo for Glass, R = 9.566^(^-1). Dry Chalk, Dry New Red Sandstone, Sandstone (Building Stone), .# = 8.882 a(0-i). Polished Limestone, R = 9.106 a* (at i). Unpolished Limestone (same block), R= i2.SoSa e (a t -i). 214 RADIATION AT Where a retains the value given in Dulong and Petit' s ex- periments, viz. a= 1.0077, an d 6 denotes the temperature of the enclosure, while / denotes the excess of temperature of the hot surface. VARIATION WITH TEMPERATURE OF QUALITY OF HEAT. 236. Having now considered the law of cooling as repre- senting with much accuracy the quantity of heat given out by a black substance at different temperatures, we come next to the relation between the temperature and the quality or nature of the heat given out. And here we may remark that the laws which connect the radiation of a black body with its temperature, both as regards the quantity and the quality of the heat given out, hold approximately for bodies of indefinite thickness which are not black, thus, for in- stance, they would hold for a metallic surface, which would represent very nearly a lamp-black surface, with the radiation diminished a certain number of times. These laws would not, however, hold exactly for a white surface, such as chalk ; for this substance behaves like lamp- black with respect to rays of low temperature, while it is white for rays of high temperature, and the consequence of this will be that its radiation will increase less rapidly than that of a lamp-black surface. In like manner, these laws will not hold exactly for coloured surfaces. Now with regard to a lamp-black surface, which, as we have seen, is the proper representative of heated surfaces, we have reason to believe that the following laws hold. i. The spectrum of the radiant heat or light given out by a lamp-black surface is a continuous one, embracing rays of all refrangibilities between certain limits on either side. Thus the spectrum of an ordinary fire is a continuous one, and in like manner that of the electric light, or of carbon at a very high temperature, is also continuous. DIFFERENT TEMPERATURES. 215 2. We have reason to believe, that as the temperature rises the spectrum of a black substance is extended in the direction of greatest refrangibility^ so as to embrace more and more of the violet and photographic rays. This extension of the spectrum is also very perceptible to the eye, for a body at first emits only dark rays or rays of low refrangibility, then it becomes red hot, after which it is of a yellow heat, and finally it becomes white hot. There is thus a very apparent change with increasing temperature in the refrangibility of the radiation ; and this is produced in the first place, as we have seen, by the addition of rays of a high refrangibility, which are (at least as far as we can judge) absent from the radiation of lower tempera- ture. But besides this, we are induced to believe that each individual ray of the low temperature is increased for the high temperature, only a ray of high refrangibility is in- creased in a greater proportion than one of low refrangi- bility, so that perhaps the average refrangibility is augmented at the same time that the total amount of radiation of any given refrangibility is also increased. Thus, the radiation from a piece of coal just below redness consists entirely of dark rays, while that from the sun embraces a large propor- tion of luminous and chemical rays, and is probably of a much higher average refrangibility than the radiation from the coal ; but the dark rays common to both bodies likewise occur in greater amount in the solar radiation, where they form, in fact, a spectrum of great heating power towards the left of the red. 237. It thus appears that the rays proceeding from a heated body do not sensibly affect the human eye until the body has attained the temperature of redness, after which the body rapidly increases in luminosity. Thus, for a range of at least 500 Fahr. above the temperature of the eye the rays of heat emitted by a body are invisible. The cause 2l6 RADIATION AT of this invisibility is rather a physiological than a physical question ; nevertheless, the suitableness of this arrangement is at once apparent, for if any other law were to hold if, for instance, the eye were affected by each substance in proportion to the difference between its radiation and that due to the temperature of the human body it is difficult to conceive how we could either enjoy the advantages of dark- ness, or experience that variety of shade and colour which is one of the chief pleasures of vision. It is also worthy of remark that by the present arrangement our safety is secured, for the eye is generally able to detect the presence of com- bustion when it occurs. RADIATION OF A PARTICLE; RADIATION OF GASES. 238. Having discussed the radiation from heated surfaces, that from thin plates or particles comes next to be considered. Take, for instance, a glass plate at a low temperature : this will stop nearly all the rays corresponding to this tempera- ture, and therefore it will behave very much like a lamp- black surface. But at a high temperature (above redness, for instance) it will pass a great many of the rays of this temperature; and hence, its proportional absorption being less, its proportional radiation compared to lamp-black will also be less. The radiation of such a plate will not there- fore increase with the temperature as fast as that from a lamp-black surface. Many other bodies beside glass possess the property of being more opaque to heat of low than to that of high temperature, and for all these the radiation will not increase with the temperature so fast as that from a black surface. The thinnest plates of solid or liquid substances which we can obtain will not, however, afford us the means of studying the radiation from a particle; in order to do this recourse must probably be had to a gas, each of whose DIFFERENT TEMPERATURES. 21 7 particles we may perhaps suppose acts for itself, and is not fettered by the neighbouring particles in the way in which it would be in the solid or liquid state. 239. In studying the radiation of gases we are led to some very peculiar laws. 1. In the first place, we may say that the general ab- sorption and radiation of gases are often small, while on the other hand the selective absorption and radiation of many of them are very strong. The feeble radiation from heated air was observed by Melloni, and the feeble absorptive power of it (and of many other gases) for light is familiar to every one. Nevertheless, by aid of electricity we are en- abled to heat a portion of any gas or vapour to a very high temperature, so as to obtain a visible spectrum from it, which we may then analyze by means of the spectroscope. Such spectra when obtained are always discontinuous, that is to say, they consist of a very intense radiation of certain disconnected spectral rays, while the intervening spaces are totally, or nearly, dark. It matters not what gas be sub- jected to analysis, the result obtained is of this nature in all cases. The spectra of all gases are thus characterised by a few bright lines on a dark background. 2. In the next place, as far as ive know at present \ the bright lines given out by any one gas have not been found to coincide in spectral position with those given out by any other gas. One or two coincidences of this kind have been suspected, but these have not been confirmed by results of a more search- ing analysis. Elaborate researches on the spectra of gases have been made by various philosophers. 3. In the third place, the spectra of gases probably remain of the same character, with certain limitations to be afterwards mentioned, throughout a very wide range of temperature. Thus we know that the vapour of metallic sodium, as soon as it has attained a yellow heat, will give out exclusively the 21 8 RADIATION AT double line D in the yellow, and it will continue to radiate this kind of heat up to the highest temperature we can produce. The same law holds for other gases and vapours, only we must make the following exception. If, for instance, one of the bright lines given out by a heated vapour be in the blue of the spectrum, and if this vapour be capable of existing at a red heat, we must not expect that it will give out the blue line at this heat, nor until the tempera- ture rises to such a degree that blue becomes one of the constituent rays of that temperature. When this is reached the blue line will be given out, and when once given out it will probably continue for all higher temperatures. 240. These laws of gaseous radiation have lately become of great practical importance. Let us recapitulate them. In the first place, the spectrum of an ignited gas consists of a few bright lines of definite refrangibility. Secondly, these lines are probably not the same for any two substances. Thirdly, the lines peculiar to any substance remain the same throughout a great range of temperature. If to these three laws we add the following chemical one, namely, that at a very high temperature most substances are decomposed, we shall soon readily perceive the great practical importance of this combination of facts. For if we already know the spectra of the various chemical elements, and if we heat a specimen of any substance pre- sented to us for analysis sufficiently to resolve it into its elements and to drive these into the state of vapour, then will the position of the bright lines of the spectrum of the flame obtained enable us to ascertain what elements were present in the substance, since each element will furnish its own peculiar lines, which are supposed to be known and recognizable. It was first remarked by Professor Swan that by means of the well-known and peculiar double line DIFFERENT TEMPERATURES. 319 D the presence of a salt of sodium may be detected in a most delicate manner; and Bunsen and Kirchhoff, who have done much more than any one else to introduce and perfect this method of analysis, remark that by means of the spectroscope the presence of less than 2iro\TroT7.inFTF f a grain of sodium ;nay probably be detected. Bunsen has also by this means discovered two new metals, namely ccesium and rubidium. Our countryman Crookes has dis- covered thallium, and Messrs. Reich and Richter indium, by the same means. An apparent exception to the law that the nature of the spectrum of a gas remains constant throughout a great tem- perature range, ought to be remarked in the case of nitrogen, which changes the nature of its spectrum at a very high tem- perature. This is viewed by some as an indication that nitrogen is in reality a compound body, since the same change takes place in the spectra of some other gases which we know to be compound. 241. Before concluding this chapter we ought to allude to the beautiful discovery of Kirchhoff, by which it has been proved that substances with which we are here familiar exist also in the atmospheres of the sun and stars. It had been observed, first by Wollaston and after him by Fraunhofer, that the solar spectrum contains a number of dark lines, while it is in other respects a continuous spectrum, and the latter observer extended his remarks to the spectra of many of the fixed stars. The origin of these lines for a long time remained a mystery, nor was this mystery diminished when it was found by Fraunhofer that a bright band corresponding in refrangibility to the double dark line D of the solar spectrum was produced by the light of a flame containing sodium. Sir D. Brewster was the first who prepared the way for the solution of this problem, by shewing that analogous (not identical) lines might be artificially produced by inter- 220 RADIATION AT posing ajar of nitrous acid gas in the path of a ray of light. The inference naturally drawn from this experiment was, that the lines of the solar spectrum do not denote rays originally wanting in the light of the sun, but are due to the absorption of his light by some substance interposed between the source of light and the spectator. It was doubtful, however, whether this stoppage of light occurred in the atmosphere of the sun or in that of our earth, until the matter was finally settled by KirchhorT, not however before the true explanation had been divined by Professor Stokes. KirchhorT found that a sodium flame which gives out on its own account the double line D absorbs a ray of the same refrangibility when it is given out by a body of a higher temperature than the sodium flame, thus producing a dark line D instead of a bright one, and he therefore conjectured that the dark line D in the light of our luminary was occasioned by the presence of the vapour of sodium in the solar atmosphere, and at a lower temperature than the source of light. This belief was strengthened by his finding that many of the dark solar lines correspond in position with the 54- DIFFERENT TEMPERATURES. 221 bright lines given out by metallic vapours, and by this means he detected the presence not only of sodium but also of iron, nickel, calcium, magnesium, barium, copper, and zinc, in the atmosphere of our luminary. In Fig. 54 we have a sketch of the appearance presented when the sun's spectrum is compared with that of the vapour of sodium. By a similar process Messrs. Miller and Huggins have detected the presence of sodium, magnesium, hydrogen, calcium, iron, bismuth, tellurium, antimony, and mercury in Aldebaran, and other elements in other stars. More lately Mr. Huggins, in directing his spectroscope to certain nebulae, was surprised to find that their light resolved itself into bright lines with a dark background, thereby indi- cating from analogy that these bodies are vast masses of incandescent gas. The position of these lines appeared to indicate that the composition of these curious bodies was a mixture of nitrogen and hydrogen, but about this there is some uncertainty. A still more recent experiment of Donati would appear to indicate that the constitution of comets is similar to that of the nebulae above mentioned, and that these erratic visitants are likewise composed of incandescent gas. This, however, is not yet well proved *. It would thus appear that through the laws of radiation we are likely to attain much information regarding the structure of the universe, both as regards the constitution and materials of celestial systems, and perhaps also as regards the internal structure of material molecules. * While this work is being printed Mr. Huggins has successfully directed his spectroscope to omet I, 1866, and he finds that the light from the nucleus consists of bright lines, appearing thus to indicate ignited gas ; on the other hand, the coma has a continuous spectrum. 222 ABSORPTION OF CHAPTER V. Radiant Heat. Further Remarks on Absorption. 242. It has already been stated (Art. 183) that the spectrum of a radiant body may be divided into three, according to three effects which rays produce. The first of these is the heating, the second the luminous, and the third the chemical, spectrum. The absorptive behaviour of substances with regard to the different rays of the spectrum is exceedingly varied in character, and forms at the same time a subject well worthy of our study both from its theoretical and practical importance. With regard to light, we know that the absorption of a substance for certain rays produces the colour of the sub- stance, and sometimes enables us to determine its com- position by means of its peculiarity of colour ; but if we were able to study the behaviour of a substance not only with respect to light but also with respect to dark heat and chemical action, it is quite clear that we should both extend our knowledge of the relation which substances bear to various kinds of rays, and also add largely to our means of discriminating between different substances. We shall now shortly study the behaviour of bodies with respect to dark heat and to light, reserving for another chapter their behaviour with regard to chemical rays. ABSORPTION OF DARK HEAT BY DIFFERENT BODIES. 243. Delaroche was the first to shew that bodies exercised a selective absorption for dark rays, or sifted a stream of dark heat passing through them ; and from this he argued that such heat consists of different kinds of rays mingled together, just as white light consists of a mixture of dif- ferently coloured rays ; and these conclusions of Delaroche have been abundantly confirmed by the experiments of RADIANT HEAT AND LIGHT. 223 Melloni. The method of analysis adopted by Melloni will be seen from the following table, although the heat is not strictly dark, being the rays from a Locatelli lamp. Transmission of i oo incident rays. Names of substances inter- posed ; thickness, unless mentioned, 2.6 millimetres. B cj 1 3'S rt vo ^ *