LIBRARY UNIVERSITY OF CALIFORNIA, Class WORKS TRANSLATED BY DR. GEORGE K. BURGESS PUBLISHED BY JOHN WILEY & SONS. Thermodynamics and Chemistry. A Non-Mathematical Treatise for Chemists and Students of Chemistry. By P. DUHEM, Corre- spondant de 1'Institut de France, Professor of Theoretical Physics at the - University of Bor- deaux. Authorized Translation by GEORGE K. BURGESS, Docteur de 1'Universiu* de Paris, As- sistant Physicist, Bureau of Standards. 8vo, xxi + 445 pages, 139 figures. Cloth, $4.00. High-Temperature Measurements. By H. LE CHATELIER, Ingenieur en chef du Corps des Mines, Professor de chimie mine'rale au > ol- lege de France, and O. BOUDOUARD, Assistant, College de France. Translated by GEORGE K. BURGESS, D.Sc. (Paris), Assistant Physicist, Bu- reau of Standards. Second Edition, Revised and Enlarged. 12010, xv + 34i pages, 79 figures. Cloth, $3.00. Frontispiece. HIGH-TEMPERATURE MEASUREMENTS. BY H. LE CHATELIEK, Ingenieur en chef du Corps des Mines, Professeur de chimie minerale au College de France, Editor of the Revue de Metallurgie, AND O. BOUDOUARD, Docteur es Sciences. AUTHORIZED TRANSLATION AND ADDITIONS BY G. K. BURGESS, D.Sc. (PARIS), Assistant Physicist, Bureau of Standards. Of THE UNIVERSITY Of SECOND EDITI&Q(38B!&&AND ENLARGED. FIRST THOUSAND. NEW YORK : JOHN WILEY & SONS. LONDON : CHAPMAN & HALL, LIMITED. 1907 Copyright, 1901, 1904, BT GEORGE K. BURGESS. ROBERT DRT7MMOND, PRINTER, NEW YORK. AUTHOR'S PREFACE TO FIRST AMERICAN EDITION. THE measurement of high temperatures was considered for a long time to be a very difficult operation and of a very uncertain precision. There were cited with admira- tion a half-dozen determinations seeming to merit some confidence. During the last few years the question has made considerable progress, and we possess to-day several sufficiently precise pyrometers whose usage is rapidly spreading among scientific and industrial laboratories. Before describing them, perhaps it will not be useless to indicate the services that they may render to science and to industry, by giving a brief summary of similar services that they have already rendered. Among the researches in pure science which result from the new methods of the measurement of high tempera- tures, of primary importance are the masterly investiga- tions of Osmond on the allotropic transformations of iron. After having precisely determined the nature of the phenomenon of recalescence, noted for the first time by Gore and Bartlett, Osmond discovered in iron two similar transformations : one, taking place in the neighborhood of 750, corresponds to the loss of magnetic properties, and the other, at about 900, is accompanied by a considerable evolution of heat. A third transformation of iron near ill iv AUTHOR'S PREFACE TO AMERICAN EDITION. 1300 has been discovered since by Ball. Soon after, Curie studied by the same methods the variation with the temperature of the magnetic properties of a great number of substances, iron among them, which possess very definite perturbations corresponding to the different trans- formation-points. Later, Le Chatelier studied the influence of temperature on the dilatation and electrical resistance of metals. The allotropic transformations are recognized by sharp points in the curves of electrical resistance and by sudden depres- sions in the dilatation curves. But these researches have not been limited to the metals and their alloys. Investigating the dilatation of the differ- ent varieties of silica, Le Chatelier was led to the discovery of a transformation of quartz at 580, above which the dilatation of this substance becomes negative, and to the discovery, still more important, of a new variety of silica distinct from tridymite, but possessing the same density and into which silex and even quartz are transformed by sufficient heating. In the same manner have been studied the dissociation of the carbonate of lime, the bromide of barium, of minium, etc. Similarly the curves of fusibility of salt mixtures have been determined, their forms indicating the existence of definite compounds or of solid solutions. Also it has been possible to distinguish, among the natural products classed under the general Jiead clay, a series of distinct chemical substances. Finally, it has been possible to pursue the study of the laws of radiation at high temperatures with a greater precision, and to establish the theory of incandescent enclosures. If we take up next the researches in industrial science, we find the number to be so considerable that it is out of AUTHOR'S PREFACE TO AMERICAN EDITION. V the question to attempt to give in this short preface the complete list. It will suffice to mention the most impor- tant among them, such as the following investigations: The fusibility of metallic alloys has been the object of a very complete memoir by H. Gautier, and of important researches by the late Sir Roberts Austen and by Heycock and Neville, Boudouard and others. The tempering of steel has been examined in all its details by Osmond, Charpy, H. Howe, Sauveur, Brinnel. Cementation by Arnold. Crystallization in the annealing of metals, in particular of iron and brass, observed by Sauveur, Stead, Charpy. And lastly the considerable number of researches made at the laboratory of the Ecole des Mines on the dilatation of ceramic pastes and of glass, by Damour, Chatenet, Grenet, Coupeau, Chautepie. Precise methods for the measurement of high tempera- tures are not limited to laboratory researches, however, but have rapidly penetrated into industrial practice. A series of investigations by Le Chatelier first made known the exact temperatures entering into the various metallurgical operations; and to-day, in the greater number of steel- works, the tempering and the annealing of the great forged pieces, cannons, plates, are no longer made without the aid of pyrometers, doing away with the workman's judgment, formerly alone consulted. In glass manufacture Damour has introduced the em- ployment of pyrometers for controlling the large furnaces and recipients, and for the regulating of the temperature of the annealing-chambers. Parville has done the same for the porcelain industry, where the use of fusible cones allowed the determination of the stopping-point of the heating but gave no contin- uous indications necessary to regulate the time of heating, VI AUTHOR'S PREFACE TO AMERICAN EDITION. and on this last depends in a large measure the quality of the products obtained, and above all the cost of fuel. In the manufacture of chemical products the precise measurements of temperature render to-day very great services; for instance, in the Deacon process for the making of chlorine, whose yield varies very greatly for slight changes of temperature. Ludwig Mond in England and the St. Gobian Company in France have the merit .of having first utilized these new scientific methods. Euchene of the Paris Gas Company controlled all the details of the manufacture of gas by numerous measure- ments of temperature. But the most remarkable of these industrial applications have been made in England under the lead of Sir Roberts Austen by applying photographic recording to the indica- tions of the thermoelectric pyrometer. Such installations at the Clarence Works of Sir Lothian Bell and at the blast- furnaces of Dowlais give a continuous record of the tem- perature of the draft and of the escaping gases. These very considerable results have been obtained within less than ten years, although the new methods of temperature measurement were known as yet to only a few scientists and engineers. It is plausible to suppose that their influence on the progress of science and industry will be still greater during the coming years. In finishing this preface, allow me to thank Dr. G. K. Burgess for having taken the trouble to translate into English our little volume. His science and his competence are for us a certain guarantee of cordial reception by American and English readers. H. LE CHATELIER. PARIS, January 10, 1901. PREFACE TO SECOND EDITION. THE subject of pyrometry has advanced very rapidly in recent years, and in preparing a new edition of the HIGH TEMPERATURE MEASUREMENTS, it has been necessary to completely revise the work. This revision has been made by the translator at the request of Prof. Le Chatelier, and the plan followed has been to leave the original text intact as far as possible and to insert the results of recent work hi the appropriate chapters, all of which have been so modified. The greatest advances have been made in optical py- rometry, and the chapter on this subject has been greatly extended and preceded by one on the laws of radiation. This material is largely taken from a paper * by Drs. Waid- ner and Burgess, and the latter desires to express his indebtedness to Dr. Waidner for permission to use this material. Considerable additions have been made to the chapters on Electrical Resistance, Thermoelectric and Gas Pyrom- etry. Brief descriptions have been added of some other pyrometers which have been considerably used in the industries, especially in the United States. The impor- * C. W. Waidner and G. K. Burgess: Optical Pyrometry, Bulletin of the Bureau of Standards, 1, No. 2, 1904. vii viii PREFACE TO SECOND EDITION. tance of standardizing pyrometers has been emphasized by a special chapter devoted to that subject. The translator wishes to express his thanks to those who have aided him by suggestions or data, and especially to Dr. Heraeus, Prof. H. M. Howe, Dr. Waidner, and Mr. Whipple of the Cambridge Company. GEO. K. BURGESS. WASHINGTON, September 6, 1904. CONTENTS. PAGE PREFACE TO FIRST EDITION iii PREFACE TO SECOND EDITION. . vii INTRODUCTION. THERMOMETRIC SCALES 3 FIXED POINTS 6 PYROMETERS. . 9 CHAPTER I. NORMAL SCALE OF TEMPERATURES. LAWS OF MARIOTTE AND GAY-LUSSAC 12 GAS-THERMOMETERS 13 REGNAULT'S EXPERIMENTS 16 RESULTS OBTAINED BY CHAPPUIS 20 NORMAL SCALE OF TEMPERATURES 22 THERMODYNAMIC SCALE 26 CHAPTER II. NORMAL THERMOMETER. SEVRES THERMOMETER 36 CALLENDAR'S THERMOMETER 42 THERMOMETER FOR HIGH TEMPERATURES 47 fx X CONTENTS. CHAPTER III. GAS-THERMOMETER. PAGE SUBSTANCE OF THE BULB 49 PLATINUM 49 IRON 51 PORCELAIN 51 GLASS 54 QUARTZ 54 CORRECTIONS AND CAUSES OF ERROR 56 CONSTANT-VOLUME THERMOMETER 56 CONSTANT-PRESSURE THERMOMETER 62 VOLUMETRIC THERMOMETER 64 EXPERIMENTAL RESULTS 66 POUILLET'S RESEARCHES 66 E. BECQUEREL'S RESEARCHES 69 RESEARCHES OF SAINTE-CLAIRE-DEVILLE AND TROOST. . . 69 VIOLLE'S RESEARCHES 71 RESEARCHES OF MALLARD AND LE CHATELIER 74 RESEARCHES OF BARUS 75 RESEARCHES OF HOLBORN AND WIEN 76 HOLBORN AND DAY'S INVESTIGATIONS 77 EXPERIMENTS OF JACQUEROD AND PERROT 79 ARRANGEMENT OF EXPERIMENTS 79 INDUSTRIAL AIR-PYROMETERS 81 INDIRECT METHODS 82 METHOD OF CRAFTS AND MEIER 82 METHODS OF H. SAINTE-CLAIRE-DEVILLE 83 METHOD OF D. BERTHELOT 86 CHAPTER IV. CALORIMETRIC PYROMETRY. PRINCIPLE 91 CHOICE OF METAL 92 PLATINUM 92 IRON 92 NICKEL, . , 93 CONTENTS. xi PAGE CALORIMETERS 94 WATER- JACKETED CALORIMETERS 95 SIEMENS CALORIMETER 97 PRECISION OF MEASUREMENTS 97 CONDITIONS OF USE 99 CHAPTER V. ELECTRICAL-RESISTANCE PYROMETER. PRINCIPLE 101 INVESTIGATIONS OF SIEMENS 101 RESEARCHES OF CALLENDAR AND GRIFFITHS 102 INVESTIGATIONS OF HOLBORN AND WIEN 103 LAW OF VARIATION OF PLATINUM RESISTANCE 104 NOMENCLATURE 107 USE AS A STANDARD 110 EXPERIMENTAL, ARRANGEMENTS 110 SOME RESULTS OBTAINED 112 SOURCES OF ERROR 114 HEATING OF THERMOMETERS BY THE MEASURING CUR- RENT 114 LAG OF THE PLATINUM-THERMOMETER 114 INSULATION ...... 114 COMPENSATION FOR RESISTANCE OF LEADS 115 PYROMETERS HAVING DIFFERENT VALUES OF d 116 CHANGES IN THE CONSTANTS 118 CONDITIONS OF USE 119 CHAPTER VI. THERMOELECTRIC PYROMETER. PRINCIPLE 120 EXPERIMENTS OF BECQUEREL, POUILLET, AND REGNAULT. . . 120 EXPERIMENTS OF LE CHATELIER 122 HETEROGENEITY OF WIRES 122 CHOICE OF THE COUPLE 124 a. ELECTROMOTIVE FORCE 124 6. ABSENCE OF PARASITE CURRENTS 126 c. CHEMICAL CHANGES.. . 126 xii CONTENTS. PAGE METHODS OF ELECTRIC MEASUREMENTS 128 METHOD OF OPPOSITION. . 128 PRINCIPLE OF THE METHOD 130 USE OF A POTENTIOMETER 131 COMPENSATION METHOD 133 GALVANOMETRIC METHOD 133 RESISTANCE OF COUPLES 133 GALVANOMETERS 135 DIFFERENT TYPES OF GALVANOMETER 139 REQUIREMENTS OF INDUSTRIAL PRACTICE 144 ARRANGEMENT OF WIRES OF THE COUPLE 146 JUNCTION OF THE WIRES 146 INSULATION OF THE COUPLE 147 COLD JUNCTION 151 GRADUATION 152 FORMULA 153 FIXED POINTS 156 RECENT RESEARCHES 162 ELECTRIC HEATING 163 HOLBORN AND DAY'S WORK 164 INDUSTRIAL APPLICATIONS 167 CONDITIONS OF USE 168 IRIDIUM-RUTHENIUM COUPLE OF HERAEUS . 168 CHAPTER VII. LAWS OF RADIATION. GENERAL PRINCIPLES 171 TEMPERATURE AND INTENSITY OF RADIATION 171 EMISSIVE POWERS 172 THE BLACK BODY OF KIRCHOFF 173 EXPERIMENTAL REALIZATION 173 REALIZATION IN PRACTICE 176 BLACK-BODY TEMPERATURE 176 LAWS OF RADIATION 177 STEFAN'S LAW 177 LAWS OF ENERGY DISTRIBUTION 179 WIEN'S LAWS 181 APPLICATIONS TO PYROMETRY. . .185 CONTENTS. xiii CHAPTER VIII. HEAT-RADIATION PYROMETER PAGE PRINCIPLE 187 POUILLET'S EXPERIMENTS 188 EXPERIMENTS OF VIOLLE 190 WORK OF ROSETTT 191 EXPERIMENTS OF WILSON AND GRAY 194 LANGLEY AND ABBOT'S EXPERIMENTS 197 CONDITIONS OF USE 193 FERY'S THERMOELECTRIC TELESCOPE 198 CHAPTER IX. OPTICAL PYROMETER. PRINCIPLE 204 KIRCHOFF'S LAW 204 MEASUREMENT OF THE TOTAL INTENSITY OF RADIATION. . . . 207 MEASUREMENT OF THE INTENSITY OF A SIMPLE RADIATION. . 207 OPTICAL PYROMETER OF LE CHATELIER 208 PHOTOMETER 208 ADJUSTMENT OF APPARATUS 212 MEASUREMENTS 213 DETAILS OF AN OBSERVATION 214 EMISSIVE POWER 214 MEASUREMENTS OF INTENSITY 216 GRADUATION 216 EVALUATION OF TEMPERATURES 220 CALIBRATION IN TERMS OF WIEN'S LAW 221 PRECISION AND SOURCES OF ERROR 221 MODIFICATIONS OF THE LE CHATELIER PYROMETER 226 FERY ABSORPTION PYROMETER 229 WANNER PYROMETER 229 DESCRIPTION AND CALIBRATION 229 SOURCES OF ERROR 232 RANGE AND LIMITATIONS 235 HOLBORN AND KURLBAUM, AND MORSE, PYROMETERS 236 HOLBORN AND KURLBAUM FORM 237 MORSE FORM. . .241 xiv CONTENTS. PAGE CONDITIONS OF USE 242 TEMPERATURE OF FLAMES 243 MEASUREMENT OF THE RELATIVE INTENSITY OF DIFFERENT RADIATIONS 245 USE OF THE EYE 245 USE OF COBALT GLASS 246 APPARATUS OF MESURE AND NOUEL 247 CROVA'S PYROMETER 249 ACTION OF LIGHT ON SELENIUM 252 CHAPTER X. EXPANSION- AND CONTRACTION-PYROMETERS. WEDGWOOD'S PYROMETER 253 EXPANSION OF SOLIDS 256 THE JOLY MELDOMETER 257 HIGH-RANGE THERMOMETERS 259 CHAPTER XI. FUSING-POINT, DILUTION-, AND TRANSPIRATION- PYROMETERS. FUSING-POINT PYROMETRY 261 SEGER'S FUSIBLE CONES 262 WIBORGH'S THERMOPHONES 267 DILUTION-PYROMETERS 268 TRANSPIRATION-PYROMETERS 268 CHAPTER XII. RECORDING-PYROMETERS. RECORDING GAS-PYROMETER 271 ELECTRICAL-RESISTANCE RECORDING-PYROMETER 274 THERMOELECTRIC RECORDING-PYROMETER 277 DISCONTINUOUS RECORDING 279 CONTINUOUS RECORDING 282 LIGHTING OF THE SLIT 283 SENSITIVE SURFACE 285 MODIFICATIONS OF SIR ROBERTS- AUSTEN'S RECORDER... 291 CONTENTS. XV CHAPTER XIII. STANDARDIZATION OF PYROMETERS. PAGE FIXED POINTS 295 SULPHUR 296 ZINC 297 GOLD 298 SILVER 300 COPPER 301 PLATINUM 302 IRIDIUM 302 OTHER METALS 302 TABLE OF FIXED POINTS 303 WATER 307 ANILINE 307 NAPHTHALINE 307 BENZOPHENONE 307 METALLIC SALTS 307 STANDARDIZATION OF PYROMETERS . . . . 308 STANDARDIZING LABORATORIES 309 ELECTRICALLY HEATED FURNACES 310 CHAPTER XIV. CONCLUSION 312 BIBLIOGRAPHY 319 INDEX. . . 337 HIGH TEMPERATURES. INTRODUCTION. WEDGWOOD, the celebrated potter of Staffordshire, the inventor of fine earthenware and of fine china, was the first to occupy himself with the exact estimation of high tem- peratures. In an article published in 1782, hi order to emphasize the importance of this question, he considered at length certain matters a study of which would be well worth while even to-day. "The greater part of the products obtained by the action of fire have their beauty and their value consider- ably depreciated by the excess or lack of very small quan- tities of heat; often the artist can reap no benefit from his own experiments on account of the impossibility to duplicate the degree of heat which he has obtained before his eyes. Still less can he profit from the experiments of others, because it is even less easy to communicate the imperfect idea which each person makes for himself of these degrees of temperature." Joining example to precept, Wedgwood made for his personal use a pyrometer utilizing the contraction of clay. This instrument, for nearly a century, was the only guide in researches at high temperatures. Replaced to-day by apparatus of a more scientific nature, it has been perhaps too readily forgotten. HIGH TEMPERATURES. Since Wedgwood, many have undertaken the measure- ment of high temperatures, but with varying success. Too indifferent to practical requirements, they have above all regarded the problem as a pretext for learned disserta- tions. The novelty and the originality of methods at- tracted them more than the precision of the results or the facility of the measurements. Also, up to the past few years, the confusion has been on the increase. The tem- perature of a steel kiln varied according to the different observers from 1500 to 2000; that of the sun from 1500 to 1,000,000. First of all, let us point out the chief difficulty of the problem. Temperature is not a measurable quantity in the strict sense of the term. To measure a length or a mass, is to count how many times it is necessary to take a given body chosen as a unit (meter, gramme) in order to obtain a complex system equivalent either as to length or mass of the body in question. The possibility of such a measurement presupposes the previous existence of two physical laws: that of equivalence, and that of addition. Temperature obeys well the first of these laws ; two bodies in temperature equilibrium with a third, and thus equiva- lent with respect to exchanges of heat in comparison with this third body, will also be equivalent, that is to say, equally in equilibrium with respect to every other body which would be separately in equilibrium with one of them. This law allows determination of temperature by comparison with a substance arbitrarily chosen as a thermo- metric body. But the second law is wanting ; one cannot, by the juxtaposition of several bodies at the same tem- perature, realize a system equivalent, from the point of view of exchanges of heat, to a body, of different tempera- ture; thus temperature is not measured, at least insomuch as one considers only the phenomena of convection. INTRODUCTION. In order to determine a temperature, one observes any phenomenon whatever varying with change of tempera- ture. Thus for the mercury centigrade thermometer the temperature is defined by the apparent expansion of mer- cury from the point of fusion of ice measured by means of a unit equal. to T ^ 7 of the dilatation between the tempera- ture of the fusion of ice and that of the ebullition of water under atmospheric pressure. Thermometric Scales. For such a- determination there are four quantities to be chosen arbitrarily: the phenome- non measured, the thermometric substance, the origin of graduation, and the unit of measurement; while in a meas- urement properly so called there is but one quantity to be arbitrarily chosen, the magnitude selected as unity. It is evident that the number of thermometric scales may be indefinitely great; too often experimenters have con- sidered it a matter of pride for each to have his own. Here are some examples of thermometric scales chosen from among many: Author. Phenomenon. Substance Origin. Unit. Fahrenheit Dilatation Mercury jVery cold 1 winter | 1/180 Ice to B. P. Reaumur Ice. . 1/80 " " " Celsius < it 1/100 " " " Wedgwood j Permanent ^ 1 contraction i Clay Dehydrated 1/2400 init. dimens. PouUlet Dilat. at const, p. Air Ice } (Normal ther.) Dilat. at const, v. Hydrogen " 1/100 (Thermodyn. scale) j Reversible | / heat -scale I Anything Heat = Ice to ' boiling-point Siemens Electric resistance Platinum Ice j The enormous differences above mentioned in the measurements of high temperatures are much more the result of the diversity of the scales than due to the errors of the measurements themselves. Thus the experiments 4 HIGH TEMPERATURES. on solar radiation which have led to values varying from 1500 to 1,000,000 are based on measurements which do not differ among themselves by more than 25 per cent. To escape from this confusion it was first necessary to agree upon a single scale of temperatures ; that of the gas- thermometer is to-day universally adopted, and this choice may be considered as permanent. The gases possess, more than any other state of matter, a property very important for a thermo metric -substance the possibility of being reproduced at any time and in any place identical with themselves; besides, their dilatation, which defines the scale of temperatures, is sufficient for very precise measure- ments; finally, this scale is practically identical with the thermodynamic scale. This last is in theory more impor- tant than all the other properties because it is independent of the nature of the phenomena and of the substances employed. It gives, too, a veritable measure and not a simple comparison; its only inconvenience is for the moment not to be experimentally 'realizable, at least rigor- ously, but it is impossible to say if this will always be the case. The adoption of the scale of the gas-thermometer does not in any way imply the obligation to use this instrument actually in all measurements. Any thermometer may be taken, provided that in the first place its particular scale has been standardized by comparing it with that of the gas-thermometer. According to the case, there will be advantage in employing one or another method ; practically also one almost never employs the gas-thermometer by reason of the difficulties inherent in its use, which result principally from its great dimensions and its fragility. For the estimation of very high temperatures the gas- scale can be used only by an indirect extrapolation in terms of some property of matter whose variation has INTRODUCTION. 5 been studied within the range of the gas-scale attainable experimentally and which variation is assumed to obey the same law at temperatures beyond which control cannot be had with the gas-thermometer. The gas-scale has not been experimentally determined above 1150 C., and extrapolations to 1600 C. may be made by means of thermocouples made of the platinum metals, assuming the law connecting E.M.F. and temperature to be the same above 1150 C. as below. Beyond 1600 C. the most infusible substances permanently alter their properties and we are forced to measure temperature in terms of the radiations coming from heated bodies for the reason that we have not been able to find any other than the radiating properties of such excessively heated bodies whose variations can be measured without destroying or permanently altering either the substance used as pyrometer or the substance examined. Perhaps also chemical methods may be employed eventually. It is in the realm of the laws of radiation and their appli- cations to pyrometric methods that some of the most re- cent and important advances in high temperature measure- ments have been made, so that, with certain restrictions which will be treated in the chapter on the laws of radiation, it is possible to measure on a common scale the tempera- tures of bodies heated to the highest attainable limits. It is our purpose, in this introduction, to pass in review rapidly the different pyrometric methods (that is to say, thermometers utilizable at high temperatures) whose employment may be advantageous in one or another cir- cumstance; we shall then describe more in detail each of them, and shall discuss the conditions for their employ- ment. But in the first place it is necessary to define within what limits the different scales may be compared to that of the normal gas-thermometer; it is the insufficiency 6 HIGH TEMPERATURES. of this comparison which is still to-day the cause of the most important errors in the measurement of high tem- peratures. Fixed Points. The standardization of the different pyrometers is the most frequently made by means of the fixed points of fusion and ebullition which have been determined in the first place by means of the gas-ther- mometer; the actual precision of the measurements of high temperatures is entirely subordinate to that with which these fixed points are known; this precision was for a long time most unsatisfactory because these fixed points could only be determined in an indirect manner with the gas-thermometer, and some of them only by aid of processes of extrapolation, always very uncertain. Recent researches, however, by various observers, in which improved methods of heating have been used, as well as greater purity of materials and more carefully constructed and calibrated apparatus, have led to most concordant results, in the determination of fixed points, even by most varied methods. Violle was the first to make a series of experiments of considerable precision, which up to the last few years were our only reliable data on the question. In a first series of researches he determined the specific heat of platinum by direct comparison with the air-thermometer between the temperatures of 500 and 1200. He made use indirectly of the relation thus established between specific heat and temperature to determine by compari- son with platinum the points of fusion of gold and silver; then, by extrapolation of this same relation, the points of fusion of palladium and of platinum. ^ . j Ag Au Pd Pt 3n 1954 1045 1500 1779 Finally, in a second series of experiments, he deter- INTRODUCTION. 7 mined by direct comparison with the air-thermometer the boiling-point of zinc. Boiling-point j 92 g n 6 Bams, chemist of the United States Geological Survey, has determined the boiling-points of several metals by means of thermoelectric couples standardized against the air-thermometer. Boiling-point j 772 o ^ 784 o 92 go Jj 931 o Mean 778 928. 5 Callendar and Griffiths, by means of a platinum resist- ance-thermometer calibrated up to 500 by comparison with the air-thermometer, have determined the following points of fusion and ebullition: . j Sn Bi Cd Pb Zn * uslon \ 232 270 322 329 421 Boiling-point j Aniline Naphthaline Benzophenone Mercury Sulphur under 760 mm. |184.l 217. 8 305. 8 356. 7 444. 5 These last figures may be compared with Regnault's, and Crafts' previous determinations: Naphthaline Benzophenone Mercury Sulphur 218 306. 1 357 445 Heycock and Neville, employing the same method, but with extrapolation of the law of resistance for platinum established only up to 450, have determined the follow- ing points of fusion: Sn Zn (99 M 5%) Sb (99%) Ag AU ^ 232 419 633 629.5 654.5 960.5 1062 1080. 5 At the Physikalische Reichsanstalt in Berlin, the ques- tion of establishing a temperature scale has received deserved attention. In the early nineties Holborn and 8 HIGH TEMPERATURES. Wien, using a thermocouple calibrated in terms of a porce- lain-bulb nitrogen- thermometer, found the fusing points : ^ . j Ag AU Pd pt on \ 970 1072 1580 1780 With the possible exception of the Pt point these results were subsequently found to be all high by Holborn and Day, who worked with a platinum-iridium bulb nitro- gen-thermometer and thermocouple, employing electric heating, two improvements that greatly increased the accuracy, and they unquestionably have obtained the results meriting the greatest confidence. Among others they determined the following: . ( Cd Zn Sb Al Ag Au Cu on (321. 7 419 630. 5 657. 5 961. 5 1064 1084 Mr. Daniel Berthelot, in a series of most skilfully exe- cuted investigations extending over several years, has recently calibrated thermocouples by comparison with a special form of gas-thermometer, making use of the varia- tion of the index of refraction with density. He has in this way found the points: f Ag Au Fusion \962 1064 ,,.,. Se Cd Zn :ion 690 778 918 Besides these primary measurements there are some very important secondary determinations, which will be discussed later. From all the results at hand we may conclude that the fixed points possessing the greatest reliability for the indirect standardization of the various thermometric scales and thus for the calibration of pyrom- eters are the following: . j Sn Zn Sb Al Ag Au Pt Ir on } 232 419 630 657 961 1065 1780 2250" -,, ... . ( Naphthaline S Cd Zn Ebullition | 217 . 9 444 . 6 778 925 INTRODUCTION. 9 We may consider the temperature scale as known with an accuracy better than: 0.5 between 200 and 500 C. 3 " 500 " 800 5 " 800 " 1100 25 " 1100 " 1600 50 above 1600 A more detailed discussion of the determination of fixed points and their reliability and ease of reproduction will be found in Chapter XIII on Standardization. Pyrometers. There have been a great number of pyrometric methods proposed, among which we shall dwell only upon those which have had considerable use or promise to be useful. Gas-pyrometer (Pouillet, Becquerel, Sainte-Claire-Deville, Barus, Chappuis, Holborn, Callendar). Utilizes the meas- urement of change in pressure of a gaseous mass kept at constant volume. Its great volume and its fragility ren- der it unsuitable for ordinary measurements ; it serves only to give the definition of temperature and should only be used to standardize other pyrometers. Calorimetric Pyrometer (Regnault, Violle, Le Chatelier, Siemens). Utilizes the total heat of metals (platinum in the laboratory and nickel in industrial works). Is to be recommended for intermittent researches in industrial establishments because its employment demands almost no apprenticeship and because the cost of installation is not great. Radiation-pyrometer (Rosetti, Langley, Boys, Rubens, Fery). Utilizes the total heat radiated by warm bodies. Its indications are influenced by the variable emissive power of the different substances. Convenient for the evaluation of very high temperatures which no thermo- metric substance can withstand (electric arc, sun). 10 HIGH TEMPERATURES. Optical Pyrometer (Becquerel, Le Chatelier, Winner, Hol- born-Kurlbaum, Morse). Utilizes either the photometric measurement of radiation of a given wave-length of a definite portion of *the visible spectrum, or the disappear- ance of a bright filament against an incandescent back- ground. Its indications, as in the preceding case, are influenced by variations in emissive power. The inter- vention of the eye aids greatly the observations, but dimin- ishes notably their precision. This method is mainly em- ployed in industrial works for the determination of the temperatures of bodies difficult of access for example, of bodies hi movement (the casting of a metal, the hot metal passing to the rolling-mill). Electric-resistance Pyrometer (Siemens, Callendar). Utilizes the variations of electric resistance of metals (platinum) with the temperature. This method permits of very precise measurements, but requires the employ- ment of fragile and cumbersome apparatus. It will merit the preference for very precise investigations in laboratories when we have a satisfactory determination of the variation ' of resistance of platinum in terms of the normal gas- thermometer. As a secondary instrument for the repro- duction of a uniform temperature scale throughout the range in which the platinum resistance thermometer can be used, it is unsurpassed in precision and sensibility. It is also now constructed in convenient form for industrial use. Thermoelectric Pyrometer (Becquerel, Barus, Le Chate- lier). Utilizes the measure of electromotive forces devel- oped by the difference in temperature of two similar thermoelectric junctions opposed one to the other. In employing for this measurement a Deprez-d'Arsonval gal- vanometer with movable coil, one has an apparatus easy to handle and of a precision amply sufficient considering INTRODUCTION. 11 the actual state of the means of standardization at our disposal in terms of the normal scale of temperature. This pyrometer, which has been used for a good many years in scientific laboratories, is rapidly spreading into general industrial use, where it renders most valuable service. Contraction-pyrometer (Wedgwood). Utilizes the per- manent contraction that clayey materials take up when submitted to temperatures more or less high. It is em- ployed to-day only in a few pottery works. Fusible Cones (Seger). Utilize the unequal fusibility of earthenware blocks of varied composition. Give only discontinuous indications. Such blocks studied by Seger are spaced so as to have fusing-points distant about 20. In general use in pottery works and in some similar in- dustries. There are a number of other pyrometers which have been found suitable in special cases or which for one reason or another have been found convenient in some particular line -of work. Some of these we shall mention, among them being the meldometer (Joly), interesting to the chemist or metallurgist for deterrnining fusing tempera- tures of minute specimens; the various industrial instru- ments based on the relative expansion of metals or of a metal and graphite used in air-blasts and metal baths ; and finally pyrometers based on the flow of air or vapor (Hobson, Uhling-Steinbart, Job). CHAPTER I. NORMAL SCALE OF TEMPERATURES. WE have seen that temperature is not a measurable quantity; it is merely comparable with respect to a scale arbitrarily chosen. The normal scale is the thermodynamic scale; but as it is impossible to realize rigorously this scale, it is necessary to have a practical one. In the same way that, besides the theoretical definition of the meter, there is a practical standard, a certain meter kept at the Bureau International des Poids et Mesures, there exists, besides the normal scale of temperatures, a practical' scale which is a certain gas-thermometer which we are going to study. Laws of Mariotte and Gay-Lussac. The laws of Mario tte and Gay-Lussac are the basis for the use of the dilatation of gases for the determination of temperatures. These two laws may be written the temperatures being measured with the mercury- thermometer. a is a numerical coefficient, the same for all gases, at least to a first approximation, and its value is 12 NORMAL SCALE OF TEMPERATURES. 13 when it is agreed that the interval between the tempera- tures of melting ice and boiling water is 100. But instead of considering the formula (1) as the ex- pression of an experimental law joining the product pv to the temperature defined by the mercury-thermometer, we may require of experiment merely the law of Mariotte and write a priori the formula in question, giving a new defini- tion of temperature approximating that of the mercury- thermometer. This new scale has the advantage that it adapts itself to the study of very much higher tempera- tures. The use of this process suggested by Pouillet was carefully studied by Regnault. The expression for the laws of Mariotte and Gay-Lussac can be put in the form (2) by calling n the number of units of quantity (this unit may be either the molecular weight or the gramme) ; R the value of the expression for unit quantity of matter taken at the temperature of melting ice and under atmospheric pressure. Gas-thermometers. The equivalent expressions (1) and (2) which arbitrarily by convention give the definition of temperature, can be utilized, from the experimental point of view, in various ways for the realization of the normal thermometer. 1. Constant-volume Thermometer. In the thermometer designated by this name, the volume and the mass are kept invariable. 14 HIGH TEMPERATURES. The expression (2) then gives between the two tempera- tures t and t the relation Po from which (3) 2. Constant-pressure Thermometer. In this case the pressure and the volume of the heated mass remain con- stant, but the mass is variable ; a part of the gas leaves the reservoir. The expression (2) then gives = * a from which It would be much more logical, instead of the classic ex- pressions constant-volume thermometer or constant-pres- sure thermometer, to say thermometer of variable pressure, thermometer of variable mass, which describe much more exactly the manner of their action. 3. Thermometer of Variable Pressure and Mass. The action of this apparatus combines those of the two pre- ceding types. A part of the gas leaves the reservoir, and the pressure is not kept constant. The expression (2) gives l+i . !L a Po~' n ~o'L + t ' a * NORMAL SCALE OF TEMPERATURES. 15 from which 4. Volumetric Thermometer. There exists a fourth method of the use of the gas-thermometer which was sug- gested by Ed. Becquerel, and presents, as we shall see later, a particular interest for the evaluation of high tem- peratures. We keep the name for it given by its inventor. The determination of the temperature is obtained by two measurements made at the same temperature, and not as in the preceding methods by two measurements made at two different temperatures one of which is supposed known. The mass contained in the reservoir is varied, and the ensuing change of pressure is observed. The expression (2) gives from which or This necessitates a preliminary determination of the con- stant R. In the particular case in which p'=0, which supposes that a complete vacuum is obtained, the preceding relation becomes simpler and is <--*-+. ....... (7) a n R 16 HIGH TEMPERATURES. The definitions of temperature given by these different thermometers would be equivalent among themselves and with that of the mercury-thermometer if the laws of Mariotte and Gay-Lussac were rigorously exact, as used to be held. The only advantage of the gas-thermometer in that case would be to extend to high temperatures the scale of the mercury-thermometer. In this way it was employed by Pouillet, Becquerel, Sainte-Claire-Deville. Experiments of Regnault. The very precise experiments of Regnault caused a modification in the then admitted ideas concerning the mercury-thermometer as well as the gas-thermometer, and have led to the definite adoption of a normal gas-thermometer. In the first place these experiments established that different mercury-thermometers are not comparable among themselves on account of the unequal dilatation of the differing glass employed in their construction. Thus they cannot give an invariable scale for the determination of temperature. In comparing them from to 100 they do not present between these extreme temperatures very great differences, 0.30 as a maximum, but at tempera- tures above 100 these differences may become considerable and reach 10. Constant- vol. Mercury-thermometer in Air-thermom- eter, P =760. Crystal. White Glass. Green Glass. Bohemian Glass. 100 + o.oo +o.oo +o.oo +o.oo 150 + .40 -0 .20 + .30 + .15 200 + 1 .25 -0 .30 + .80 + .50 250 + 3 .00 + .05 + 1 .85 + 1 .44 300 + 5 .72 + 1 .08 + 3 .50 350 + 10 .50 + 4 .00 NORMAL SCALE OF TEMPERATURES. 17 The numbers figuring in this table indicate the quan- tities by which it is necessary to increase or diminish the temperatures given by the air-thermometer in order to have them correspond with those which were observed with the different mercury-thermometers. It was thus impossible to define the practical scale of temperatures in terms of the mercury-thermometer. The use of the gas-thermometer became necessary. But Regnault recognized that it was not possible to take a single coefficient of dilatation a, independent of the nature of the gas, of its pressure, and of the mode of dilatation utilized. The coefficient of expansion at constant volume (a) and the coefficient of expansion at constant pressure (/?) are not identical. This follows from the fact that the law of Mario tte is not rigorously exact; we have in reality pv=p Q v +e, e being a very small quantity, but not zero. The experiments of Regnault permitted him not only to detect but to measure this variation of the coefficient of expansion. Here are, for example, the results which he found for air between and 100: Volume Constant. Pressure Constant. Pressure. 266 0.003656 273.6 760 0.003671 272.4 760 3655 272.8 2525 3694 270.7 1692 3689 271 2620 3696 270.4 3655 3709 269.5 For air at 4. 5 Rankine obtains, from the experiments of Regnault, the formula pv=p v +Q.OQ8l63^ ' I, CD being the atmospheric pressure. 18 HIGH TEMPERATURES. These coefficients vary also from one gas to another, as is shown by the following table, taken also from Regnault's experiments : MEAN COEFFICIENT BETWEEN AND 100. Volume Constant. Pressure Constant. Pressure, mm. 760 3655 760 760 760 760 3589 760 Pressure. 0.003665 3708 3667 3667 3668 3688 3860 3845 AIR. 272.8 760 269.5 2620 HYDROGEN. 272.7 760 2545 CARBON MONOXIDE. 272.7 760 NITROGEN. 272.6 CARBONIC ACID. 271.2 760 259 2520 SULPHUROUS ACID. 259.5 760 980 0.003671 3696 36613 36616 272.4 270.4 273.1 273.2 3669 272.5 3710 3845 3902 3980 296.5 259.5 253.0 251.3 These experiments show that the easily liquefiable gases have coefficients quite different from those of the per- manent gases. For the permanent gases the coefficients for constant volume differ much less among themselves than those for constant pressure; for the former the extreme deviation does not exceed T7 Vo J f r the latter it is three times as great. Setting aside) air, which is a mixture and which contains more easily liquefiable oxygen, the coefficients for constant volume of H 2 , N 2 , and CO are identical. NORMAL SCALE OF TEMPERATURES. 19 Finally, for hydrogen the coefficient of expansion does not vary with the pressure. The inequality of the coefficients of expansion, however^ does not prevent us from taking any gas whatever to define the scale of temperature, provided we apply to it the proper coefficient determined by experiment between and 100. The scales are identical, if the coefficients of expansion do not vary with the temperature. This is the conclusion to which Regnault came from a comparison of thermometers at constant volume, differing by their initial pressure or the nature of the gas. Here are the results obtained, starting from the fixed points and 100, by the aid of the following formulae: pv=nRT, p Q v=nRT , p m v=nRT lw , ICO AIR-THERMOMETER. Po=751 mm. Po = I486 mm. Degrees. 156.18 Degrees. 156.19 259.50 259.41 324.33 324.20 PRESSURE =760 MILLIMETERS. Air- thermometer. Hydrogen- thermometer. Air- thermometer. (XV thermometer. Degrees. 141.75 Degrees. 141.91 Degrees. 159.78 Degrees. 160.00 228.87 228.88 267.35 267.45 325.40 325.21 322.8 322.9 20 HIGH TEMPERATURES. The deviations do not exceed 0.2, a value that Regnault estimated not to exceed the limits of error of his experi- ments; he concluded from this that one gas may be used as well as another, and he took air for the normal ther- mometer. Nevertheless his experiments on sulphurous acid had shown a very marked variation of the coefficient of expan- sion of this gas with the temperature. The following table gives the mean coefficient at constant volume be- tween and t: t a. 98.0 0.0038251 102.45 38225 185.42 37999 257.17 37923 299.90 37913 310.31 37893 By analogy it is permissible to suppose that a similar effect should take place with -the other gases; but the differences were then too small, and the degree of precision of the methods of Regnault insufficient to detect it. Results Obtained by Chappuis. This effect has been demonstrated by experiments of very great precision made at the Bureau International des Poids et Mesures, at Sevres. Chappuis has found, between and 100, systematic deviations between thermometers of hydrogen, nitrogen, and carbonic acid, filled at under a pressure of 1000 mm. of mercury. Hydrogen Ther. N Ther. H Ther. N Ther. CO 2 Ther. - 15 -0.016 -0.094 000 + 25 +0 .011 +0 .050 + 50 +0 .009 +0. 059 + 75 +0 .011 +0 .038 + 100 Of THE UNIVERSITY Or BMAL SCALE OF TEMPERATURES. 21 In this table, taking as definition of the temperature the hydrogen-thermometer at constant volume, the num- bers in the last two columns indicate the deviations observed with the thermometers of nitrogen and carbonic acid; it is certain that these deviations are systematic. These results allow of. the determination of the mean coefficients of expansion: t a (Hydrogen) 100 0.00366254 a (Nitrogen). 0.00367689 367466 (Carbonic Acid). 0.00373538 372477 Thus the coefficients decrease with rise of temperature, while remaining higher than that of hydrogen, to which they tend to approach. The more recent work of Chap- puis and Harker and others in the establishment of a normal scale of temperatures for high temperatures will be discussed in the following sections. In the interval 100, the values given above, calcu- lated from Chappuis' data of 1888, may not be absolutely DIFFERENCE BETWEEN SCALES OF NITROGEN- AND HYDROGEN- THERMOMETERS. tii. vol. = const., 100 ems. Temp. Cent. Callendar. 1903. Chappuis. 1902. Rose-Innes. 1901. Lehfeldt. 1898. + 20 + .006 + .005 + .002 + .011 + 40 + .009 + .008 + .002 + .017 + 50 + .009 + .010 + .002 + .019 + 60 + .008 + .009 + .002 + .019 + 80 + .005 + .004 + .001 + .015 22 HIGH TEMPERATURES. exact, but they are probably very nearly correct. Some of the later results are given below; those marked Cal- lendar are calculated by him from the data of Kelvin and Joule using a modified formula; Chappuis' results are from his latest determinations (1902) while those of Lehrfeldt and Rose-Innes are calculations involving special ther- modynamical assumptions. Normal Scale of Temperatures. It results from these experiments that the different scales furnished by the various gas-thermometers are not rigorously identical; the deviations between and 100 are very small, but their existence is certain. It becomes necessary, therefore, in order to have a scale of temperature rigorously defined, to make a choice' of the nature of the gas, of its manner of dilatation, and of its initial pressure. The normal thermometer selected by the Bureau Inter- national des Poids et Mesures to define the practical scale of temperatures, and everywhere adopted to-day, is the hydrogen thermometer, operated at constant volume and filled with gas at 1000 millimeters of mercury at the tem- perature of melting ice. For high temperatures this definition is inadmissible, because we would reach such pressures that the apparatus could not withstand. The use of the method at constant volume, that is to say, at invariable mass, is besides bad on account of the permeability of the coverings at high temperatures. It would be of great advantage to be able to employ a gas other than hydrogen and operate the thermometer at variable mass. In the actual state of experimentation at high tempera- tures, it is impossible to have results exact to about 1 and indeed, practically, we are far from arriving at this precision. It is very likely that we can, under these con- ditions, employ indifferently for the construction of the NORMAL SCALE OF TEMPERATURES. 23 normal thermometer any permanent gas whatsoever. According to the preceding experiments, all the gases would have a dilatation slightly greater than that for hydrogen, and their coefficient of expansion, which de- creases with rise of temperature, would approach that for hydrogen. For determining experimentally the error possible with a normal thermometer thus modified, we possess actually but little data. Crafts has compared in the neighborhood of 1500 the expansion at constant pressure of nitrogen and carbonic acid, and found for this latter the mean coefficient 0.00368 in assuming 0.00367 for nitrogen. The experiments were made by displacing in a Meyer's tube nitrogen by carbonic acid, or carbonic acid by nitro- gen. 10 cc. N 2 displace 10 cc. CO 2 displace 10.03ofCO 3 9.95ofN a 10.01 9.91 10.00 9.98 10.03 9.93 9.95 10.09 Mean 9.94 Mean 10.02 The two measurements give positive and negative differ- ences of the same order of magnitude; but it should be noticed that the observed deviation (-j^-jr on an average) hardly exceeds the possible error of observation. How- ever it may be, carbonic acid, which differs much from the permanent gases at ordinary temperatures, no longer so differs in an appreciable degree at 1500. Violle has made some comparative measurements on the air-pyrometer used at constant pressure and constant 24 HIGH TEMPERATURES. volume in his determinations of the specific heat of plati- num. Vol. Constant. Press Constant. Difference. 1171 1165 6 1169 1166 3 1195 1192 3 There was on an average a deviation of only 4 between the two modes of observation, and the greater part of this deviation should be laid to accidental variations of the gaseous mass resulting from the permeability of the cover- ings. Chappuis has made an exhaustive experimental study of the divergences of gases from the normal scale, and he finds that the coefficient of nitrogen (at const, vol.) gradu- ally diminishes as above stated (p. 21), but that at about 75 C. it reaches a limiting value equal to aum =0.00367380 and it may be assumed that above this temperature the gas is in a perfect state. The mean coefficient at constant volume for this gas between and. 100 is o- 100 =0.00367466 and the limiting value for an initial pressure P =0 is a Po=Q =0.0036613. This follows from the divergence that Chappuis and Harker found for the constant-volume nitrogen-ther- mometer from the normal scale of temperatures, in terms of the initial pressure; their experiments gave -5- = 1.32 10~ 8 per mm. change in pressure, NORMAL SCALE OF TEMPERATURES. 25 Such a normal scale of temperature for the nitrogen-ther- mometer is given by finding the coefficient a, at C. for a pressure. P ' which the gas would have supposing it to remain perfect in the range 0100. If P = 100 cm., P 100 = 136.7466 cm., whence P ' = 100.0086 and a = ,' = 0.00367348 if a Um =0.00367330 as stated above. Nitrogen at constant pressure gives /?/? -/= 1. 19 10- 8 per mm. dp and A^ = 0.0036612. The divergences from the normal scale in this case are about double those at constant volume, and the diver- gences between the unconnected scale and the theoretical scale of the constant-volume thermometer whose constants are given above and which represents the normal scale of temperatures, are proportional to the temperature measured from 100 and have the following values: At 100 0.000 200 023 300 047 400 070 These deviations are evidently very slight and are entirely negligible within this range for practically all pyrometric uses. We shall see, however, that at 1000 this correction may assume a certain importance. For hydrogen, the limiting values given by D. Berthe- lot are: aiim =0.0036625, Aim =0.0036624, and the deviations of this gas from the normal scale are immaterial. 26 HIGH TEMPERATURES. The experiments of Chappuis and Harker were carried out at the International Bureau of Weights and Measures and included a comparison of the platinum-resistance and nitrogen-thermometers up to 500 C. and a determination of the sulphur boiling-point, to which questions we shall return. We can then affirm that, in employing any permanent gas with any mode of dilatation, we shall not differ cer- tainly by more than 5 at 1000 from the temperature of the normal scale, and in reality the deviation will be without doubt much less, and should not reach 1. Theoretically it would be preferable to use hydrogen under reduced pressure, which would certainly not give deviations of 1 from the normal scale ; but there is always the danger of the passage of this gas through the cover- ings, and of its combustion by oxygen or oxides. Practically it would be better to take nitrogen, whose expansion deviates little from that of hydrogen, less than the deviation of air. Callendar has suggested the use of helium or one of the other newly discovered inert, mqnatomic gases, as they diverge less than nitrogen from the hydrogen scale, cannot dissociate and do not pass through metals. For high temperatures the normal thermometer -will be, then, one of nitrogen or other inert gas. Thermodynamic Scale. It is defined, in terms of Car- not's principle applied to a reversible cycle working between two sources at constant temperatures, by the relation 1. Approximate Expression. Consider Carnot's cycle formed, as is well known, of two isotherms and two adia- NORMAL SCALE OF TEMPERATURES. 27 batics, and let us seek the quantity of heat absorbed fol- lowing the isotherm 7\. From Joule's experiments we have approximately Q,=Afpdv. The laws of Mariotte and Gay-Lussac give where t is the temperature of the gas-thermometer; then, p a Similarly, Q Equation (1) becomes But the experiments on adiabatic expansion give pv r = const., and combining with the laws of Mariotte and Gay-Lussac, pr-i.t~r = const. 28 mail TEMPERATURES. Consequently depends only on the ratio -*, which is the Po to same the whole length of the two isotherms. Thus or ft' ft'" ft' 7 ?"' Equation (2) then takes the very simple form 1 7\_g + \ that is to say, the ratio of the absolute thermodynamic tem- peratures is equal to the ratio of the absolute temperatures of the gas-thermometer; and if in the two scales it is agreed to take equal to 100 the interval comprised between the temperatures of melting ice and the vapor of boiling water, we have, at any temperature, the equality T=-+t. a But this is only a first approximation, for we have em- ployed relations that are but roughly so: the laws of Joule, Mariotte, and Gay-Lussac. 2. Reconsider the problem by a more exact method. Since T differs very little from -, and since the laws NORMAL SCALE OF TEMPERATURES. 29 of Mariotte and Gay-Lussac are nearly true, we place, fol- lowing a method of calculation indicated by Callendar, (f> being a very small function of p and of T (thermo- dynamic temperature). We have then, between the temperature of the gas- thermometer and the thermodynamic temperature, the relation which will permit of passing from one scale of tempera- ture to the other if we know the corresponding value of <. Consider, as before, Carnot's cycle, and let us deter- mine the heat of isothermal expansion in a more exact manner, by utilizing the experiments of Joule and Thom- son on the expansion through a porous plug, and those of Regnault on the deviations from Mario tte's law. We write for this that the changes in energy between two given isothermal states are the same, either for the reversible expansion or for the expansion of Joule and Thomson. Q.-A pi' Po' e being the very feeble change in heat of the gas accom- panying its passage through the porous plug, in the experiment of Joule and Thomson. We get from this Q^=A I vdp-\- I ~C--dp (at constant temperature), (3) JPI' J &P 30 HIGH TEMPEtiATUttES. for d(pv)=pdv + vdp. The relation pv=RT(l-) gives for the value of v HI /H| rx "= (l-$i which, substituted in equation (3), leads to Similarly, we have If we introduce these values in the expression for Carnot's cycle, after division by T v and T we should find an identity: p The law of adiabatic expansion gives In order, then, that the expression reduce to an identity it is necessary that 1 ds . D < , de 11 -= AR < or ^' Referring to the experiments on air of Joule and Thom- son, we have *-0.001173A @', NORMAL SCALE OF TEMPERATURES. 31 p being the atmospheric pressure, and T the tempera- ture of melting ice. This is still an approximate result, for we have depended upon the experiments of Joule and Thomson and on the law of adiabatic expansion; however, the approximation is more close. If it seems sufficient for air, it is certainly not so for carbonic acid. Neither is the formula rigor- ously exact for air. Callendar has calculated the correction to make to the air-thermometer readings by extrapolation up to 1000, and he found the following results: Readings of Centigrade Thermometer. Volume Constant. Pressure Constant. # dt * It 0.001173 0.001173 100 0.000627 0.000457 200 393 0.04 225 0.084 300 267 0.09 127 0.20 500 147 0.23 52 0.47 1000 54 0.62 12 1.19 The deviations of the air-thermometer at high tem- peratures are thus very slight if concordance is estab- lished at and 100 and we have seen that in the case of nitrogen the experiments of Chappuis and Harker have shown the same to be true for this gas. In an experi- mental investigation, not yet completed, on the dilata- tions of nitrogen, air, oxygen, carbon monoxide and carbonic acid throughout the ran'ge 1000 Jacquerod and Perrot find, using a quartz bulb at constant volume, that the coefficients of the first three remain excessively close together throughout this range and that the coeffi- cient for carbonic acid, although less than in the 100 32 HIGH TEMPERATURES. interval, remains considerably greater than for the other gases. Callendar, in a recent computation based upon the work of Kelvin and Joule and the experiments of Chappuis and others, arrives at the following values for the scale corrections for the best thermometric gases: SCALE CORRECTIONS FOR GASES, ASSUMING =273.10. Constant Pressure, 76 cms. Constant Volume p\ = 100 cms. Temp. Cent. Helium. Hydro- Nitro- Air. Helium. Hydro- Nitro- Air. gen gen. gen. - 150 4-0.073 + 0.084 + 0.945 + 0.901 -0.026 + 0.013 + 0.195 + 0.186 - 100 + .030 + .022 + .328 + .314 - .012 + .005 + .080 + .076 - 50 + .009 + .006 + .090 + .086 - .004 + .002 + .024 + .023 - 20 + .003 + .002 + .025 + .024 - .001 + .000 + .007 + .007 + 20 -.0016 -.0009 -.0141 -.0134 + .0008 -.0003 -.0043 + .0041 + 40 - .0022 -.0013 -.0195 -.0186 + .0011 -.0004 -.0059 + . 0056 + 50 -.0022 -.0013 - .0195 -.0186 + .0011 -.0004 - . 0059 + .0056 + 60 -.0021 -.0012 -.0180 -.0172 + .0011 - . 0004 - .0054 + .0053 + 80 -.0013 -.0008 -.0113 -.0108 + .0007 -.0002 -.0038 + .0034 + 150 + .0054 + .0029 + .043 + .041 '-.0031 + .0010 + .0143 + .0136 + 200 + .0128 + .0068 + .101 + .096 -.0076 + . 0024 + .035 + .033 + 300 + .0332 + .0165 + .243 + .232 -.203 + .0059 + .088 + .084 + 450 + .071 + .034 + .495 + .472 -.047 + .013 + .189 + .180 + 1000 + .243 + .104 + 1.53 + 1.46 -.187 + .044 + .646 + .616 The above table indicates that for the gases hydro- gen and helium no attention need be paid to the thermo- dynamic correction, for it is quite negligible for the whole temperature range for these two gases. All the gases are also seen to have a greater correction at constant pressure than at constant volume. Again it is to be noted that at small initial pressures these corrections will be proportionally reduced, and finally that it is only in the most refined work that this correction need be applied, as in the establishment of a fixed point in pyrometry as the gold fusing-point. NORMAL SCALE OF TEMPERATURES. 33 D. Berthelot has indicated a simple method for calcu- lating this thermodynamic correction for any gas. For a constant volume thermometer: T-T =tl\ a 10 ~^ \ 373273 + J/' T being the absolute temperature of melting ice (273. 10), T the absolute temperature sought corresponding to the centigrade temperature t given by the gas-thermometer in question at an initial pressure. For other pressures p the correction to t must be multiplied by ^. For the constant-pressure thermometer . 273646 + * 373273 + * The value of a depends upon the critical constants of the gas and is = 64 '7? where R is the gas constant (here ) , T c and p c the * 27 o . I/ critical pressure and temperature respectively. TABLE OF CRITICAL CONSTANTS. PC l - 10 9 = 322Z + 1 A7t 2 between and 100, where the curvature is of the same order as for metals. In work at 1000 C. the expansion correction is reduced from over 20 with porcelain or platinum to about 1, and its uncertainties become therefore negligible, permit- ting a great increase in accuracy. Several investigations 56 HIGH TEMPERATURES. are now under way using quartz bulbs, and a final judg- ment as to its availability will have to await the com- pletion of this work. Corrections and Causes of Error. 1. Thermometer at Constant Volume. We must now render more precise the formula of the air-thermometer, by taking account of the variations of volume of the bulb, of the surrounding air- temperature which changes the density of the mercury, and finally of the volume of the waste space. We have three series of observations to make in order to determine a given temperature: (1) 100100 PV=nRT ........ (3) Putting the first two series serve to determine . a It is preferable, except in researches of very great precision, to take from previously obtained results, and not to make the observations at 100, unless one does so to check his experimental skill. Dividing the third equation by the first, we have the relation PV_ HA,V nRT = nT P 7 H Q AV, n RT Q n T > where H and H are the heights of mercury, A and J the densities of this metal. For a first approximation let us neglect the differences GAS-PYROMETER. 57 between V and V , n and n , J and J . We shall have then an approximate value T' for the temperature sought : r= l'f/ (5) for Let us find now the correction dT to T 7 ' to obtain the exact temperature. In order to find this, take the loga- rithmic differential of (4) : dT dJ dV dn Then determine the values of the different terms; let t l and t 2 be the absolute temperatures of the surroundings when the bulb is at the temperatures T' and T . = -o.oooi8( 2 - * ^(porcelain) = 0.0000135., dV ^-=0.0000135(7 7/ -!T ), ^0 by neglecting the variations of volume of the bulb due to changes of pressure, 58 HIGH TEMPERATURES. \ 3 dn = x 2 -x l n Q n in calling x 2 and x x the number of molecules contained in the waste space at the temperatures t 2 and t v We have in fact, N being the total mass contained in the apparatus, n=N-x 2 , To determine x 1 and x 2 : tr Q =x^Kt^j Pe=x 2 Rt 2 , n V Q \t 2 In noting that we have Put *=^ After substitution we have '-T Q 6 n Q V Q \ t t t . GAS-PYROMETER. 50 These successive transformations are for the purpose of making evident from the formula: 1. The ratio between the waste space and the total volume: ==-; "o 2. The temperature measured: T'-T ; 3. The variation of the surrounding temperature 0; which are the three essential factors on which depends the correction in question. Formula (6) then becomes: ' = ~ 0.00018(< 2 - y + 0.0000135( T - T ) _ /T 7 ' T* ft *T* T* C-V -i 7 / Let us take a numerical example in order to show the importance of these correction terms in the three follow- ing cases: T'-T^ 500, T- T = 1500. In taking *=27+273=300, 2^ = 10, we have ^500=- 1.4+ 5.15 + 13.1= 16.85, ^1000=- 2.3 + 17.0 +38.2= 52.9, d7 T l500 =-30.7 + 35.7 +90.0 = 122.5. These figures show the very great importance of the waste space, whose exact volume it is impossible to kno\ T! is 60 HIGH TEMPERATURES. method of computation of the corrections by logarithmic differentials is only approximate, and is not sufficient for real measurements, but it renders more clear the general discussion of the causes of error. Let us see what uncertainty in the temperature may result from the uncertainty which there may be in the volume of the waste space. In reality there is a continu- ous passage from the high temperature of the pyrometer to the surrounding temperature on a length which may vary from 10 to 30 centimeters, according to the thickness of the walls of the furnace. The volumes of the bulb and of the waste space which should be taken in order that the above formulas be exact should be such that the real pressure is equal to the pressure that would exist in sup- posing that a complete and sudden change of tempera- ture took place at a definite fictitious point, separating the heated part from the cold part of the apparatus. The probable position of this point is estimated, and, if the estimation is poorly made, two errors are committed, one on the real volume heated and the other on the waste space, errors equal and of opposite sign so far as the volume is concerned. To calculate this error, as in the case of the corrections, we may employ the method of logarithmic differentials. Applying the same formula as before, we find for the dT relative error ~=~ : dT = dV/T'-T 6 T ~ ~ V \ t t and neglecting the second term of the parenthesis, which is relatively very small, dT dV/T'-T \ GAS-PYROMETER. 61 Letting the section of the capillary tube be equal to I sq. mm., the volume of the bulb 100 cc., and assumig an uncertainty of 100 mm. in the position of the tran- sition-point, a value often not exaggerated, we find the following errors in the temperatures: We thus see that at 1000 the error resulting from the uncertainty in the origin of the waste space may reach several degrees for a bulb of 100 cc. A second cause of error results from the changes of mass following the ingoings and outgoings of gas. As before, we have dT == _dn T ~ n ' Consider the experiments of Crafts. There enters per hour at 1350 in a bulb of porcelain of 100 c.c., 0.002 grm. of water- vapor, or 0.225 milligramme-molecules; the initial volume enclosed at the start is 4.5 milligramme- molecules : f .235=0.05, which leads to an error of dr i350 o= 70 (about) for an experiment lasting one hour. This computation demonstrates clearly the enormous errors which may result from the penetration of an outside 62 HIGH TEMPERATURES. gas during the time of one hour, a length of time much less than that of an ordinary experiment. It is true that this error decreases rapidly with rise of temperature, and it is very probably zero at 1000, if there is no break in the glazing. 2. Constant-pressure Thermometer. We still employ the same formula (4) : nRT which gives for a first approximation n Calling ^ and t 2 the surrounding absolute temperatures corresponding to T and 7\, u^ and u 2 the corresponding volumes of the waste space and of the reservoir, we have, for the determination of n and n , the relations: ft/Q J.T /J , . , h'h n=N-x 2 =n -(x 2 -x 1 ), HAu 2 As before, there is a correction to be applied to the approximate temperature T f thus obtained: d dH dJ dV T'~ H+ J + V ' an expression the values of whose terms are known. GAS-PYROMETER. 63 Let us see now the causes of error and discuss their im- portance. The error resulting from the uncertainty in the bound- ary of the hot and cold volumes is ~ P + y ' GAS-PYROME TER. 65 In general dP is in the neighborhood of 15 mm. of mercury, which gives Also, dV ^-=0.0000135(7 T/ -7 7 ), Calculating this correction for different temperatures, we have ^1000=- 8.5, dT 15W =- .35. Let us compute now the error which comes from the uncertainty in the position of the line of separation of the warm part and the cold part of the apparatus; it is, besides, the only remaining one: dT__dV T'~ V As before, assuming the higher limit to be y dT 1 r'lOOO' which leads to ,777 _n 77 a 500 ~ U ' 'l dT im = l .27, dr=2 .77. 66 HIGH TEMPERATURES. From every point of view, this method is thus preferable to the others. This whole discussion of the sources of error in the measurement of temperatures aims merely to obtain a deter- mination of the temperature of the pyrometer employed. But this temperature is in itself not the real object of the measurements; it is but an intermediary to arrive at a knowledge of the temperature of certain other bodies supposed to be in thermal equilibrium with the pyrom- eter. Now this equilibrium is extremely difficult to realize, and it is more often the case that there is no way of being sure of the exactitude with which it has been obtained. Here is then a new source of error very important in the measurement of temperatures, especially of high tem- peratures, at which radiation becomes an important con- sideration. Within an enclosure whose temperature is not uniform, which is true for the majority of furnaces, there may exist enormous differences of temperatures between neighboring parts. One cannot too strongly insist upon the presence of this source of error, with whose existence too many investigators have not suffi- ciently occupied themselves. Experimental Results. We shall study now the experi- ments made by various savants, and we shall see in what degree the conditions of precision indicated in the course of this account have been realized. Experiments of Pouillet. Pouillet was the first to make use of the air-thermometer for the measurement of high temperatures; he obtained very good values for the epoch at which he worked. His pyrometer was made of a platinum bulb, of ovoid form, of 60 cc. capacity, to which was gold-soldered a platinum capillary tube of 25 cm. in length; continu- ous with this tube was another of silver of the same length GAS-PYROMETER. 67 fastened to the manometer. The joining of the platinum and silver tubes was made by means of a metal collar (Fig. 5). The waste space had thus a volume of 2 cc. FIG. 5. The manometer was made up of three glass tubes em- bedded at their lower ends in a metallic piece; the first tube serving as a measurer was gradu- ated in cubic centimeters, the second constituted the manometer properly speaking, and the third served to fill the apparatus. A cock conveniently placed per- mitted variation of the quantity of mercury contained in the apparatus (Fig. 6). The principle of this appa- ratus is the same as that of the more recent Regnault manometer; this lat- ter differs from the manometer of Pouillet only in the suppression of the third tube, which is replaced by a bottle joined to the emptying-cock by a rubber tube. Errors: 1. According to Pouillet, it was impossible to carry the measure- ments up to 1200; there was complete disaccordance with the readings of the mercury-thermom- eter. He attributed this non-agreement to the condensa- 68 HIGH TEMPERATURES. tion of air on the platinum. Becquerel showed later that this was due to the presence of water-vapor in the insuffi- ciently dried air. 2. Not being able to use the 100 mark for the determi- nation of the coefficient of expansion of air, Pouillet took the number 0.00375, given by Gay-Lussac, instead of the correct number, 0.00367. This is the principal source of error in his measurements. The following table permits a comparison of his results for the specific heats of platinum with those obtained by Violle: 100 300 500 700 1000 1200 Pouillet, a =0.00375. . a= 0.00367... Violle 0.0335 32 323 0.0343 336 535 0.0352 345 347 0.0360 353 359 0.0373 366 377 0.0380 373 389 Fusing-points. Pouillet 's points are far less good: determinations of fusing- Gold 1180 (too high by 115) Silver 1000 ( " " " 40) Antimony 432 (too low by 200) Zinc 423 (good) The possible sources of error are the following: 1. Introduction of hydrogen into the platinum bulb, which should raise too high the temperature-measurement and diminish the specific heat of platinum; the fusing- points of gold and silver are too high. 2. Equilibrium of doubtful temperature with the fur- nace as arranged. A glass tube, heated from below by coal, would necessarily be more strongly heated near the base; it would then have been necessary, in order to have accurate measurements by this arrangement, certainly GAS-PYROMETER. 69 very irregular as to temperature, that the substance and the thermometer be in the same conditions with respect to radiation (Fig. 7). For antimony the error is certainly due to some particular cause; or perhaps the very impure metal was mixed with lead, or there may have been a mistake in computation. Nevertheless the number 432 was the only one used up to the recent memoir of Gautier on the fusibility of alloys. Experiments of Ed. Becquerd. This savant took up and con- tinued the work of Pouillet with the same apparatus. But at the close of a discussion with H. Sainte-Claire-Deville on the ques- tion of the permeability of plati- num, he made use successively of pyrometers of iron and of porcelain. The results obtained with platinum seem, however, to be far the best. Pyr. of Pt. Pyr. of Porcelain. Boiling-point of zinc 930 (good) 890 Fusing-point of silver 960 " 916 Fusing-point of gold 1092 1037 The figures for gold differ among themselves by about 25, more or less. It is difficult to explain these differences, which are probably due to inequality of temperature between the pyrometer and the metal under investigation, resulting perhaps from a difference in their emissive powers. Experiments of H. Sainte-Claire-Deville and Troost. They, after their discussion with Becquerel, made numer- FIQ. 7. 70 HIGH TEMPERATURES. ous experiments with the porcelain air-thermometer; they obtained very discordant results, which they did not publish at the time. They placed the most confidence in the determinations made by the aid of the vapor of iodine (we shall speak of this later) ; but when the inaccuracy of this method was pointed out, they made known the results that they had obtained for the boiling-point of zinc. They employed a crucible of plumbago having a capacity of 15 grms. of zinc; the metal was added anew as fast as it evaporated. The crucible was placed in a furnace filled with coal. Around the pyrometer was arranged a covering of fire-clay ; but this arrangement was quite insufficient to eliminate errors due to radiation. The same measurements were repeated with different gases. Figures obtained : Gas. First Series. Second Series. Third Series. Air From 945 to 955 940 to 948 928 to 932 Hydrogen " 925 to 924 916 to 924 C&rboiiic 8/cid 1067 1079 The deviations seem to be a function of the nature of the gas, which is inexplicable; it would be necessary to admit of an enormous dissociation of the carbonic acid in order to explain the temperatures found with this gas. Later this method was modified. The gas enclosed in the pyrometer was removed by means of the mercury-pump, either warm or after cooling. But this method did not possess any real advantages; the entrance of the gas and vapors during the reheating is not avoided ; besides, during the cooling, there is danger of the entrance of air by leak- GAS-PYROMETER. 71 ing of the cock placed at the outlet of the pyrometer. Troost found in this way 665 for the boiling-point of selenium; this figure is too high. As in the case of the determination of the boiling-point of zinc, the arrangement for heating did not protect sufficiently against the radiation from the outer surfaces. Violle's Experiments. Guided by H. Sainte-Claire- Deville, whom his successive failures had instructed in the difficulties of the problem, Violle has made a series of measurements which are among the best up to the present time. He made use of a porcelain thermometer, and he worked simultaneously at constant pressure and constant volume. The agreement of the two numbers shows if the mass has remained constant; this is the equivalent of the method of Becquerel. The most serious objection that can be made to these observations is as to the uncertainty of the equality of tem- peratures of the pyrometer and of the substance studied placed beside the former; from this point of view, however, these experiments, made in the Perrot furnace, were much more satisfactory than those made in coal-furnaces pre- viously employed. 1. A first series of determinations was of the specific heat of platinum. A platinum mass of 423 grm. was put into a Perrot muffle alongside the pyrometer, and when the mass was in a state of temperature-equilibrium it was immersed, either directly in water or in a platinum eprouvette placed, opening upward, in the midst of the calorimeter-water. In the first case the experiment was made in a few seconds; in the second it lasted fifteen minutes, and the correction was as high as 0.3 per 10; the results, however, were concordant. At 787 two experi- ments gave 0.0364 and 0.0366; mean, 0.0365. At 1000 twelve experiments were made employing the 72 HIGH TEMPERATURES. method of immersion; the numbers found vary from 0.0375 to 0.0379; mean, 0.0377. Near 1200 the measurements were made at constant pressure and at constant volume. Temperature Temperature Specific Heat at Constant at Constant Mean. of Volume. Pressure. Platinum. 1171 1165 1168 0.0388 1169 1166 1168 .0388 1195 1192 1193 .0389 The mean specific heat may be represented by the formula C < =0.0317+0.000006-. The true specific heat is equal to = 0.0317 + 0.000012-*. at Violle used these determinations to fix, by extrapolation, the fusing-point of platinum, which he found equal to 1779. He measured for that the quantity of heat given out by 1 grm. of solid platinum from its fusing-point to 0. For this purpose a certain quantity of platinum is melted, into which is plunged a spiral wire of the same metal, and, at the instant that the surface of the bath solidifies, by aid of this wire a cake of solid platinum is lifted out and immersed in the water-calorimeter. Repeat- ing the determination of this fusing-point, Holborn and Wien have found more recently 1780. The latent heat of fusion of platinum is equal to GA S-PYROMETER. 73 74.73 c.1.5; this number results from five determina- tions. 2. A second series of experiments was on the specific heat of palladium; the determinations were made, in part by comparison with platinum, in part by the air-thermometer. The results obtained by the two methods are concordant. The mean specific heat is given by the formula C ' =0.0582 +D.000010 - 1. The true specific heat is equal to ^ = 0.0582 + 0.000020 - 1. dt The fusing-point was found equal to 1500; the more recent experiments of Holborn and Wien give 1580. This difference can be explained by impurities in the metal and absorption of furnace-gases. The latent heat of fusion of palladium, measured by the same experiments, was found to be 36.3 calories. 3. In another series of experiments Yiolle has deter- mined the boiling-point of zinc. He employed an ap- paratus of enamelled casting, heated in a triple envelope of metallic vapor; the top was covered with clay and cow-hair to prevent superheating of the coverings. The measurements were made with pressure and volume simultaneously variable. Volume of bulb 294 . 5 cc. Volume of gas let out 184 . 3 cc. Waste space 4.7 " Pressure 892.3 mm. 7 T =929.6 t 3. 8 t . .: 7. 7 H 760 . 5 mm. H 759 . 5 mm. Bams, Holborn and Wien found numbers very close to 930. 74 HIGH TEMPERATURES. 4. A last series is relative to the fusing-points of metals, which were determined by comparison with the total heat of platinum: Silver 954 (too small by 10) Gold 1045 ( " " " 20 ) Copper 1050 ( " " " 15 ) Experiments of Mallard and Le Chatelier. In their investigations on the temperatures of ignition of gaseous mixtures, Mallard and Le Chatelier made use of a porce- lain pyrometer, which was exhausted, then air was let in and the gaseous volume thus absorbed was measured. It is possible to reach 1200 without noticing any breaking down of the porcelain; but this giving way is complete at 1300 under the action of the vacuum. This method was used in the following way to measure the temperatures of ignition of gaseous mixtures. The air was exhausted from the apparatus, and the tempera- ture was measured by the air- volume which filled it; the air was again exhausted and the apparatus was filled with the gaseous mixture. Whether or not there was ignition was known by the comparison of the volume of the mix- ture with that of the air introduced under the same con- ditions of temperature, at least in the cases of mixtures burning with contraction. The pyrometer used had a capacity of 62 cc., after de- duction of the waste space (1 cc.) ; the following table gives the volumes of air corresponding to different temperatures : 400 26.7cc. 600 20.6 800 16.7 1000 14.1 1200., . 12.2 GAS-PYROMETER. 75 In admitting that the measurements of volume be made to 0.1 cc., one should have a precision of only 10 in 1000 on account of the insufficient volume of the thermometric reservoir. Experiments of Barns. This American savant devised a rotating apparatus, remarkable for its uniformity of tem- perature, but he applied it directly only to the standard- ization of thermoelectric couples. He worked at constant pressure. By means of couples graduated in this way, he has determined the boiling-points of zinc (926-931) and of cadmium (773-784); the boiling-point of bis- muth was found equal to 1200 under a reduced pressure of 150 mm., which would give under atmospheric pressure by extrapolation 1500. Fig. 8 represents the longitudinal section of Barus' apparatus. It is composed essentially of a porcelain FIG. 8. pyrometer containing an interior tube in which is placed the couple. The pyrometer fixed at a point of its stem is held stationary. It is surrounded by a muffle of casting whose general shape is that of revolution about the axis 76 HIGH TEMPERATURES. of the pyrometer; this muffle is composed of two similar halves held by means of iron collars, and can be given a motion of rotation about its axis of figure, in such a manner as to assure uniformity of heating. It is heated by gas-burners placed below. An outer covering of fire- clay keeps in the heat about the iron muffle. Experiments of Holborn and Wien. Holborn and Wien have made a very complete standardization of the thermo- electric couple Pt Pt-Rh proposed by Le Chatelier. They made use of a porcelain reservoir of about 100 cc. capacity, terminating at its two ends in capillary porce- lain tubes. The thermoelectric junction is placed inside the bulb, and each of its wires is led out by one of the lateral tubes; this arrangement allows of determining at various points the real temperature of the waste space whose volume is 1.5 cc. They worked at constant volume, with a very low initial pressure so as always to have depression; they were able to reach 1430. Above 1200 they could make but a single observation with one pyrometer; below this, about ten observations. They determined the coefficient of expansion of their porcelain, a product of the Berlin works, and found it equal to 0.0000045, the identical number given by Le Chatelier for the Bayeux porcelain. They made use of this pyrometer, employing as inter- mediary a couple, to fix the fusing-points of certain metals : Silver 970 Gold 1072 Palladium 1580 Platinum 1780 These figures, at the time they were obtained, were counted among those which seemed to merit the most GAS-PYROMETER. 77 confidence; however, it is necessary to note that the volume of the bulb was too small to assure a very great accuracy. We shall return to these experiments when treating of electric pyrometers. Holborn and Day's Investigations. The work of estab- lishing the gas-scale upon a satisfactory basis was continued at the Reichsanstalt by Holborn and Day, who also deter- mined the thermo-couple scales in terms of that of the nitrogen constant- volume thermometer as well as estab- lishing several fixed points. Their preliminary work was done with porcelain bulbs at temperatures above 500 C. using nitrogen and hydro- gen and with a bulb of Jena borosilicate glass No. 56 m filled with hydrogen for temperatures below 500. Por- celain bulbs glazed outside and also inglazed bulbs were used. Errors due to changes in the bulbs were detected by taking "zero" readings and also by the simultaneous use of thermocouples. Salt baths were used up to 900 at first, but later electric heating was employed in all the high temperature work. The hard glass bulbs of about 167 cm. capacity showed less changes, after annealing, than the irregularities in the thermocouple measurements, due to^the lack of sen- sitiveness of the latter at low temperatures; and these glass bulbs were found preferable to those of porcelain up to 500 C. The precision attainable with thermo- couple control was about 0.6 C. Porcelain bulbs of 100 cc. capacity glazed inside and out, filled with hydrogen and heated to only 700, gave very discordant results due apparently to chemical action between the hydrogen and the walls of the bulb and to water-vapor generated. Used with nitrogen and heated electrically to about 1100 C. the mean difference between 78 HIGH TEMPERATURES. the observed and calculated values was 1.5 C. Far less satisfactory results were obtained with porcelain glazed only on the outside. A first series of experiments with a metal bulb were made with a 20 per cent iridium alloy of platinum, the bulbs being cylindrical of 208 cc. volume and 0.5 mm. wall and the waste space was considerably reduced over that of the porcelain bulbs. The electric heating oven was also improved by winding it logarithmically so that at 1150 the temperature distribution was constant to 3 over that portion of the oven containing the bulb. This was still further equalized by the presence of the metallic bulb; also at very high temperatures the tend- ency to equilibrium through radiation balances more nearly the losses by end conduction. Temperature con- trol to 0.l C. at 1000 C. may be realized electrically with care. A precision of better than 1 C. was then obtained, and the conclusion seemed warranted that the metallic bulbs in an electrically-heated furnace, where no gases or other materials acting upon platinum were in contact with it, were superior to any form of porcelain bulb. Their later work consisted in a determination of fixed points using the thermocouple as intermediary, after having found the coefficient of expansion of the material of their bulb and shown that the bulb underwent no deformation after heating. The correction for expansion amounts to 30 at 1000 and 40 at 1150. The expan- sion was determined for a 50 cm. bar in a comparator which could be heated electrically to 1000 C. Although no change in volume of the thin-walled bulb could be detected on cooling, a temporary yielding of the glowing walls under the comparatively high pressure might have taken place, so a bulb having walls 1 mm. thick was substituted, the composition being 90 Pt-10 Ir. This bulb was as satisfactory as the first. GAS : PYROMETER. 79 The results obtained by Holborn and Day for the fixed points, as well as their work with thermo-elements, will be discussed later. Experiments of Jacquerod and Perrot. Only a pre- liminary publication of this work has as yet been made. Using a quartz bulb filled at constant volume successively with nitrogen, air, oxygen, carbon monoxide, and carbonic acid, and employing an electric resistance furnace, results agreeing to 0.3 were obtained for the fusing-point of gold with the first four gases using a common coefficient of expansion based on Chappuis limiting value and using varying initial pressures. The use of quartz reduces the correction for the expansion of the bulb to 2 at 1000. This work shows that in the range 0-1100 C. the coeffi- cients of expansion of these gases are practically identical. Arrangement of Experiments. The discussion that we have just held permits us to define certain conditions to which should conform new experiments necessary to further the accuracy of fusing and boiling temperatures used as fixed points for the standardization of other pyrometers. Before Holborn and Day had demonstrated the super- iority of an iridium alloy of platinum for the bulb, it seemed preferable to recommend that the bulb of the thermometer be of porcelain enamelled inside and out, as were the bulbs made at Sevres for certain experiments of Regnault and of H. Sainte-Claire-Deville. Quartz may be found preferable up to 1200 C. The capacity of the bulb should be as nearly as may be as great as 500 cc., the condition necessary in order that the error resulting from the waste space be certainly less than 1. It may be desirable to immerse the manometer and other exposed parts in a water-bath to insure a constant temperature. 80 HIGH The thermometric gas will be nitrogen, or perhaps helium. The volumenometer method should be employed, or any equivalent method which does not suppose the invariability of the gaseous mass, and the greatest changes of pressure compatible with the resistance of the material will be produced. Up to 1200 a high vacuum should be em- ployed, since there is no danger of deforming the bulb. Finally, most careful precautions will be taken to assure the equilibrium of temperature between the reservoir of the pyrometer and the body whose temperature it is desired to measure. Barus' arrangement seems to be theoretically entirely satisfactory, but it. is quite complicated and costly. One can still make use of muffles completely surrounded with flames, as in the fabrication of porcelain ; the tempera- ture there is very uniform. But their use offers a serious practical difficulty: the stem of the pyrometer, although well protected, frequently breaks at the point where it passes through the compartment of flames. It will be more practical, perhaps, to make use of liquid baths non-volatile fused salts for example, kept in contin- uous agitation, in which plunge at the same time the ther- mometer bulb and the body whose temperature is to be found, the heating being obtained by the combustion of gas in a Perrot furnace, or by an electric current passing through a coil immersed in the bath. If one has to use an ordinary gas-furnace, Perrot furnace, or, better, a Leger furnace, it will be necessary to explore by means of a thermoelectric couple the distribution of temperature in the whole region utilized. Satisfactory and uniform heating of a gas thermometer at high temperatures is secured only by the immersion of the bulb in an electrically heated furnace, the wind- ings of which, preferably of platinum foil, are so spaced as to secure uniformity of temperature. GAS-PYROMETER. 81 Industrial Air-pyrometers. There have been attempts to construct air-thermometers suitable for industrial usage, the argument sometimes being advanced that a gas-pyrometer is per se better than any other. As we have seen, however, there is probably no physical instru- ment which is more difficult to employ satisfactorily, and any seeming gain in making direct use of an air thermometer for industrial use is wholly illusary. Other evident objections are fragility, uncertain correction due to the waste space, and the development of small and often unperceived leaks. Furthermore an empirical calibration is necessary so that such an instrument does not carry the gas-scale about with itself. Among the instruments that have been considerably used is Wiborgh's air-pyrometer, shown in Fig. 9. A lens- shaped V reservoir is open to the air before an obser- vation is taken, but when a temperature is to be read this lens is closed to the outer air and collapsed by a lever L, thus adding a definite mass of air to the bulb V of the thermometer; the resulting pressure is transmitted to a dial as in an aneroid barometer; provision is made for automatically correcting for variations in the pressure and temperature of the atmosphere. 82 HIGH TEMPERATURES. INDIRECT PROCESSES. We shall place in this list various experiments in which the laws of the expansion of gases have been used only in an indirect way, or have been extended to vapors. Method of Crafts and Meier. It is a variation of the method of H. Sainte-Claire-Deville and Troost, consisting in removing the gas by means of a vacuum. Crafts and. Meier displaced the gas of the pyrometer by carbonic acid or hydrochloric acid, gases easily absorbable by suitable reagents. Hydrochloric acid is the more convenient, for its absorption by water is immediate; but there is to be feared at high temperatures its action on the air with formation of chlorine; it is preferable to employ nitrogen in place of air. The apparatus (Fig. 10) consists of a porcelain bulb, whose inlet is large enough to let pass the entrance-tube of the gas, which reaches to the bottom of the bulb. This arrangement increases consider- ably the influence of the waste space and consequently diminishes the pre- cision of the determinations. This method is especially conve- nient for observations on the densi- ties of vapors which are made by the same apparatus; it then allows of having an approximate idea of the temperatures at which the experiments FlG - la are made. Crafts and Meier have in this way determined the varia- tions in density of iodine vapor as a function of the tem- perature. CD [ GAS-PYROMETER. 83 Regnault had previously proposed a similar method, without, however, making use of it. 1. One fills with hydrogen an iron vessel brought to the temperature that one desires to measure, and the hydrogen is driven out by a current of air; at the outlet of the metallic reservoir the hydrogen passes over a length of red-hot copper, and the water formed is absorbed in tubes of sulphuric acid in puniice-stone and weighed. This method, very complicated, is bad on account of the per- meability of the iron at high temperatures. At the same time, he proposed the following method: 2. An iron bottle containing mercury is taken; the vessel, being incompletely closed, is heated to the desired tem- perature and then allowed to cool, and the remaining mercury is weighed. This method is also defective on account of the permeability of iron at high temperatures; the hydrogen of the furnace-gases can penetrate to the inside of the recipient and drive out an equivalent quantity of mercury-vapor. Methods of H. Sainte-Claire-Deville. 1. This savant tried in the first place to measure temperature by a process analogous to that of Dumas' determination of vapor- densities. He took a porcelain bulb full of air, and heated it in the enclosure whose temperature was wanted, and sealed it off by the oxyhydrogen flame. He measured the air remaining by opening the bulb under water and weighing the water that entered, or else he determined merely the loss in weight of the bulb before and after heating. Observations taken on the boiling-point of cadmium gave 860. The data for the computation were as follows : H = 766.4 mm. Volume of bulb =285 cc. Volume of remaining air = 72 cc. 84 HIGH TEMPERATURES. The computation may be made also in this way: Let 17 be the surrounding temperature; 7 7 =273+17= 290. ooc r = 290X^=1150. The correction due to the expansion of the porcelain is 0.0000135X850 = 13, which gives for the temperature of boiling cadmium t= 1150 -273 -13 = 864.* The figure 860 is too high. There are in these experiments two possible sources of error: non-uniform heating on account of radiation, and the possibility of the existence of water-vapor in the bulb. Besides, the small weight of the air and the difficulty of closing the recipient absolutely tightly render the experi- ments very delicate. 2. In a second method, which has the advantage of replacing the air by a very heavy vapor, Deville returned to the idea of Regnault, consisting in utilizing the vapor of mercury; but he ran against a practical difficulty. He had replaced the permeable iron recipients by porcelain recipients; the mercury condensed in the neck of the pyrometer and fell back in cold drops which caused the bulb to break. * This result differs slightly from that given by Sainte-Claire- Deville, because we have taken as coefficient of expansion of porcelain the most recently obtained value; besides, the assumed temperature of the surroundings, 17, differs perhaps from the real one, which is not given. GAS-PYROMETER. 85 For this reason he abandoned mercury and replaced it with iodine; the return of a cold liquid was completely obviated by reason of the nearness of the boiling-point of this substance (175) and its fusing-point (113). A large number of observations were made by this method; the boiling-point of zinc, for example, was found to be equal to 1039. The data were : H =758. 22 mm. Volume of bulb .............. "... =277 cc. Increase in weight. Iodine air. . . = . 299 grm. Volume of remaining air .......... =2 . 16 cc. Density of iodine-vapor .......... =8. 716 The computation can be made in the following way: If the temperature of the surroundings is 17, the theoretical weight of the iodine-vapor contained in the bulb at this temperature would be 27S 1.293X8.716X0.277X^=2.92 grms. The weight of iodine remaining in the reservoir is, taking note of the correction to be made resulting from the 2.16 grms. air which occupy 8.9 cc. at 930, 070 0.299 + 1 .293(0.277 - 0.00216)^ = 0.634 grm. If there had been no air, the weight would have been 277 -I- 8 Q 0.634 X =0.652 grm. = 1290. 86 HIGH TEMPERATURES. Making the correction for the expansion of porcelain (15), we have T' = 1290 - 273 - 15 = 1002. The difference between the result of this computation and that of Deville comes from similar reasons to those noted above (page 84, note). This method is quite faulty, as the iodine does not obey the laws of Mariotte and Gay-Lussac. The vapor-density of this substance decreases with rise of temperature, this effect being attributed to a doubling of the iodine mole- cule. This fact was established by Crafts and Meier and confirmed by Troost. Temperatures ......... 445 850 1030 1275 1390 Densities ............. 8.75 8.08 7 5.76 5.30 ~.. 1 0.92 0.80 0.66 0.66 Troost found 5.70 at the temperature of 1240. If, in the preceding computation, we take 7.8 as the density of iodine at the boiling-point of zinc, we then find a temperature lower than 1*50, which is far too low. Method of Daniel Berthelot. All the preceding methods are limited by the impossibility of realizing solid envelopes resisting temperatures higher than 1500. D. Berthelot has devised a method which, at least in theory, may be applied to any temperatures, however high, because there is no envelope for the gas, or at least no envelope at the same temperature. It is based on the variation of the index of refraction of gaseous mass heated at constant pressure; the velocity of light depends upon the chemical nature and the density of this medium, but is independent of its physical state. A gas, a liquid, or a solid of the GAS-PYROMETER. 87 same chemical nature produces a retardation of the light dependent only upon the quantity of matter traversed; this law, sensibly true for any bodies whatever, should be rigorously exact for substances approaching the condition of perfect gases. This retardation is measured by the dis- placement of interference fringes between two beams of parallel light, the one passing through the cold gas, the other through the hot gas. In reality Berthelot employs a null method; he annuls the displacement of the fringes in changing at constant temperature the pressure of the cold gas until its density is equal to that of the gas in the warm arm which is at constant pressure. Apparatus. There is a difficulty arising from the neces- sity of separating the light into two parallel beams, then reuniting them without imparting a difference of phase M> T < \fi/ i I \ Tl P 93% Tl * <% ffl ^ 1 E 9 FIG. 11. which renders the fringes invisible with white light, is done in the following way (see Fig. 11); This 88 HIGH TEMPERATURES. A beam of light db falls on a mirror MM' , which breaks it up into two parallel beams, bf and cd; in order to separate the beams so as to be able to place apparatus conveniently with respect to them, a prism P gives to the beam bf the direction gh ; one can thus secure a separation of 92 mm. A second prism P l brings the beam cd into Im, and after reflection from a second mirror, AfjM/, the fringes are observed in a telescope focussed for parallel rays. The tubes containing the gases are placed at T and TV It is evidently necessary that the prisms P and P 1 be perfectly made. A preliminary adjustment is made with yellow light, then it is perfected with white light. The tube at variable pressure is closed by two pieces of plate glass, as is also the warm tube; these four plates should be absolutely alike. The warm tube is heated by a vapor-bath at low temperatures, by an electric current passing through a spiral at high temperatures. But there is a difficulty in that 'in the warm tube there exists a region of variable temperature between the warm zone and the cold atmosphere. To eliminate the influence of this variable zone there are inside the warm tube two tubes containing running cold water whose distance apart can be changed; it is assumed that the variable region remains the same, and that dis- tance between the two tubes gives the warm column actually utilized. It follows that the comparative lengths of the warm column and of the cold column (this latter remaining constant) are not the same; the formula to be used will be somewhat more complicated. n being the index of refraction of a gas and d its density, we have GAS-PYROMETER. 89 In the constant-pressure tube d p 9 ' To obtain the invariability of the fringes it is necessary that (n l -n )L=(n'-n Q )l, L being the length of the cold tube, and I the displace- ment of the warm tube; k(d l -d Q )L=k(d'-d )l, T i a > 5. Lummer and Pringsheim found the following limits of temperature as given by the Wien relation la: *m J^max ^min Electric arc. . . 7 fi 4200 abs 3750 abs Nernst lamp 1 2 2450 2200 Auer burner. . . 1 2 2450 2200 Incandescent lamp 1 4 2100 1875 Candle 1 5 1960 1750 Argand burner 1 55 1900 1700 Lummer and Pringsheim also heated a carbon tube electrically to about 2000 C. and observed the tempera- ture inside simultaneously with instruments making use of the several radiation laws; THE LAWS OF RADIATION. 185 Method. T absolute. (2310 Photometric < 2320 (2330 i 2330 Total radiation \ 2345 (2325 Energy maximum \ 2320 This complete concordance at such a high temperature between the different radiation methods gives further con- fidence in the legitimacy of their indefinite extrapolation for non-luminescent bodies. Waidner and Burgess have also found that this accord probably exists at the tem- perature of the electric arc, 3600 C. Applications to Pyrometry. It is evident that theoret- ically any of these laws and their various consequences might be used as a basis of pyrometry, but practically it is not convenient to make use of all of them. The dis- placement law (X m T = A) and the maximum-energy law (E m T~ 5 = B) of Wien are well-established relations, but in practice it is exceedingly difficult to construct instru- ments of sufficient sensibility to give any considerable precision, and any industrial pyrometer using these prin- ciples is out of the question .at the present time. The reason of the lack of sensibility with the relation X m T=A is due to the fact that the exact position of the wave length possessing the maximum of energy is very difficult to locate, especially at relatively low temperatures; see Fig. 39. The value of the maximum energy could perhaps be measured more readily, but, as this quantity varies as the fifth power of the temperature, there would hardly be any preference for this over the former method. There have been, however, several most convenient, simple, and very accurate instruments devised which are 186 HIGH TEMPERATURES. based either on the use of Stefan's law (E or Wien's distribution law \J = cf* > e~~w) , either directly or indirectly, and in the two following chapters we shall treat of these at some length. Crova suggested that the upper limit of the spectrum of an incandescent body might be used as a measure of this temperature, and Hempel has recently tried this method with a special form of spectroscope, using a luminescent screen for observing when the upper spectrum limit is beyond the visible radiations; but, as compared with the photometric and radiation pyrometers, only crude results can be obtained. CHAPTER VIII. HEAT-RADIATION PYROMETER. Principle. The quantity of heat that a 'body receives by radiation from another body depends on certain condi- tions relative to each of the two bodies, which are: 1. Temperature; 2. Surface; 3. Distance apart; 4. Emissive and absorbing power. In order to utilize heat radiation for the determination of temperatures, one measures a heat change produced on the body used as an instrument by the body to be studied ; this heat change is either a rise of temperature or a re- sulting phenomenon, such as a change of electrical resist- ance, thermoelectromotive force, etc. The quantity of heat given off is proportional to the radiating surface S, and varies inversely as the square of the distance I. a-lc 8 -ifi -V'E d * q_lc--lcj 2 -ic , d being the diameter of the radiating surface S, E its emissive power. Now, -j is the apparent diameter of the object; the quantity of heat radiated depends then upon the solid angle under which the object is seen. Any instrument 1S7 188 HIGH TEMPERATURES. making use of the intensity of radiation must, therefore, have a receiving device of sufficiently small area so that it may be completely covered by th desired radiation. The emissive power E is very variable from one substance to another as we have seen, and for the same substance variable with the temperature. It would be desirable to determine this, but that is difficult, often impossible, especially at high temperatures, although some advance has been made in this direction as we have seen in the preceding chapter. The coefficient ft" is a function of the temperature alone, which expresses the law of variation of the radia- tion with he temperature. This law should be determined in the first place. It is on the more or less exact knowl- edge of this law that the entire accuracy of the results de- pends. We have seen that Stefan's law (p. 177) satisfies all requirements for the measurement of total radiation, although the early experimenters, working before the establishment of this law, were obliged to express their results empirically. Let us see now what are the experimental arrangements which have been used to measure the intensity of heat radiation; these measurements have had for their only aim, until recently, the determination of the sun 's temperature, but they may serve other uses. Pouillet's Experiments. Before Pouillet, Gasparin had already made some trials. His apparatus consisted of a hollow brass sphere mounted on a foot and blackened ; a thermometer was used to measure the rise in temperature of the water contained in the sphere. The advantage of this arrangement was that the apparatus was always mrned properly toward the sun. The pyrrheliometre .of Pouillet consists of a calorimeter which measures directly the heat received by radiation HEAT-RADIATION PYROMETER. 189 (Fig. 40) . A very thin silver box is carried by a hollow tube, cut along a generatrix to let the thermometer be seen. The box is of 100 mm. diameter by 15 mm. height; it contains 100 cc. of water. At the lower part of the box is located a metallic disk of the same diameter as the box, and serving to turn the apparatus toward the sun ; it suffices, in fact, for the shadows of the box and disk to coincide exactly in order that the system be properly pointed. A knob serves to turn the apparatus about its axis in order to stir the water. Finally a support gives the means of placing the system in any desired orienta- tion. To take an observation, the ap- paratus is set up and shielded from the sun's action by means of a screen; the readings of the thermometer are taken for five minutes; the screen is removed and the thermometer is read for five minutes ; the screen is put back, and a new set of readings of the thermometer for five minutes is taken. The first and the third sets furnish the corrections due to the surroundings. Pouillet observed in this way a rise of temperature of 1 in five minutes. In the determination of the temperature of the sun it was evidently necessary to take into account the heat absorbed by the atmosphere (it is about 20 per cent of the total radiation from the sun). Pouillet found by this method 1300 for the temperature of the sun. FIG. 40. 190 HIGH TEMPERATURES. Experiments of Violle. Violle makes use of an actino- metre, whose principle is quite different from that of the preceding apparatus; one observes the stationary equilib- rium of a thermometer receiving simultaneously radiation from an enclosure at fixed temperature, and that from the hot substance to be investigated (Fig. 41). The apparatus consists of two spherical concentric coverings of brass, in which a water circulation may be set up at constant temperature, or ice may be substituted for water. The inner covering of 150 mm. diameter is blackened inside. The thermometer has a spherical bulb whose diameter varies from 5 to 15 mm.; the surface of FIG. 41. the bulb is also blackened. The scale is divided into fifths of a degree. The entrance-tube carries a diaphragm pierced with holes of different diameter; on the extension of this tube is located an opening closed by a ground- HEAT-RADIATION PYROMETER. 191 glass mirror slightly blackened, which permits of deter- mining that the solar rays fall quite exactly upon the ther- mometer bulb. The establishment of the temperature equilibrium re- quires fifteen minutes, and the differences of temperature observed vary from 15 to 20. Yiolle found in this way, for the temperature of the sun, figures varying from 1500 to 2500. Pouillet and Violle made use of Dulong and Petit 's law of radiation, q = a', that the discoverers had established by observations reach- ing only to 300. The constant a may be determined for each apparatus by a single experiment made at a known temperature. This law, as we shall show farther on, is not exact, so that, according to the temperature used to determine the con- stant, a different value of the latter is found, and conse- quently also different values at temperatures calculated, assuming this law to hold. This is the reason for the differences between the three figures, 1300, 1500, and 2500, of Pouillet and Violle. They correspond to deter- minations of the constant obtained by means of prelimi- nary experiments made at the temperatures of 100, 300, and 1500. The elder Secchi, making use of Newton 's formula, still more inexact, found for the sun's temperature several millions of degrees. Work of Rosetti. The Italian scientist, Rosetti, was the first to grasp the fundamental importance of the choice 192 HIGH of the law assumed for radiating power; he showed that a graduation made by an experiment at 300 gave for the temperature of a body heated in the oxhydrogen flame: 46,000 if one uses the law of Newton ; 1,100" " ;" " " " Dulong and Petit. Now the temperature of the oxyhydrogen flame is about 2000. This physicist used a thermoelectric pile whose sensi- bility could be changed without touching the element; in the apparatus of Violle it is necessary, on the contrary, to change the thermometer, a proceeding which renders the observations comparable with difficulty. The pile (Fig. 42) consists of twenty-five sheets of bismuth and antimony; these sheets are very thin, for the whole of the apparatus is but 5 mm. on a side. The whole is enclosed in a small metallic tube. FIG. 42. To make an experiment there is placed before the pile a screen filled with water, which is removed at the instant of taking an observation. HEAT-RADIATION PYROMETER. 193 A preliminary calibration made with a Leslie's cube of iron filled with mercury that is heated from to 300 gave the following results: Excess of the Temperature of 32. 8 ................... 10 112 .8 .................... 55 192 .8 ................... 141 .9 272 .8 ................... 283 .5 Newton's law and that of Dulong and Petit giving no concordance between the numbers observed and those computed, Rosetti proposed the formula Q = aT\T-6)-b(T-0), where T= absolute temperature of the radiating body, = the absolute temperature of the surroundings. This formula with two parameters permits necessarily a closer following of the phenomenon than a formula with but a single parameter. y_0 Deflections Deflections Computed. Observed. Dulong's Law. Rosetti's Law. 50 A= 17.2 4+2.12 A-0.23 100 46.4 +0.95 150 90.1 -2.12 +0.70 200 151.7 +4.82 +0.99 250 234.7 +2.83 -0.12 Rosetti showed later that the formula he proposed did not lead to absurd results for higher temperatures. A mass of copper was heated to redness in a flame, and the temperature was estimated by the calorimetric method (a quite uncertain method, as the variation of the specific heat of copper is not known). The two methods gave 194 HIGH TEMPERATURES. respectively 735 and 760. This difference of 25 is less than the experimental uncertainties. Disks of blackened metal placed in the upper part of a Bunsen flame gave, according to the formula, temperatures of the order of 1000; oxy chloride of magnesium in the oxyhydrogen blast-lamp gave 2300. All these numbers are possible. Rosetti, using this formula, found 10,000 for the tem- perature of the sun, this figure resulting from an extra- polation above 300. Experiments of Wilson and Gray. These physicists measured the intensity of radiation by means of a thermo- electric couple, a method first conceived by Deprez and d'Arsonval. A movable coil made of two different metals (silver and palladium) is suspended by a silk cocoon fibre between the poles of a magnet. The solar radiation is allowed to fall upon one of the junctions, while upon the other junction is directed a source of heat which exactly balances the first. As the temperature of this auxiliary source is necessarily the lesser, it is necessary that the apparent angle which it subtends at the galvanometer be the greater. Wilson and Gray used an apparatus similar to the radiomicrometer of Boys. The suspending fibre is of quartz; the metals employed are bismuth and antimony: the electromotive force so produced is twenty times greater than that obtained with "the palladium-silver couple. The metallic strips R and R' (Fig. 43) are very thin (0.1 mm.), which renders the construction of the apparatus quite delicate. In order to protect the movable coil against air- currents, it is enclosed in a metallic case (Fig. 44) ; an open tube lets pass in the radiation; diaphragms set inside this tube prevent air -disturbances Instead of measuring, as may be done, the deflection of HEAT-RADIATION PYROMETER. 195 the mobile parts, the investigators preferred to employ a null method making use of another radiation, that from a modification of the meldometer of Jolly, an apparatus used also for the graduation of the radiomicrometer. The AM R'. FIG. 43. FIG. 44. meldometer (Chapter X) consists of a strip of platinum heated by an electric current; the dimensions are as fol- lows: 102 mm. in length, 12 mm. in breadth, and 0.01 mm. thick. This strip they placed in the midst of an enclo- sure surrounded by water. Fastened at one end, it is held in place at the other end by a spring and carries on this end a lever to which is fixed a mirror arrangement serving to optically amplify the variations in the length of 196 HIGH TEMPERATURES. the strip resulting from its heating by the passage of the more or less intense current. The relation between the change of length and the tem- perature is determined by means of the fusion of very small fragments ( l / 10 milligramme) of bodies whose fusing-points are known. Wilson and Gray used the following, which for the gold and palladium are certainly too low: Silver chloride 452 Gold 1045 Palladium 1500 With this apparatus they apparently verified, up to the fusion of platinum, the law of radiation given by Stefan, E=k(T'-T 4 ). For the purpose of graduation, the meldometer was removed to a distance, so that its action on the radio- micrometer was always the same, and it was assumed that the intensity varies as the inverse square of the distance. It is besides necessary to know the emissive power of platinum ; Wilson and Gray took as starting-points the results given by previous experiments: t Emissive Power. 3000 & 600 o 800 o And by extrapolation they found 1/2.9 at the temperature of 1250, temperature which balanced the solar radiation, with the somewhat large apparent angle subtended by the meldometer. In admitting, then, with Rosetti and Young, a zenith absorption of 30 per cent, the temperature of the HEAT-RADIATION PYROMETER. 197 sun, supposed to be a black body, was found equal to about 6200. This figure must be considerably uncertain, on account of the errors involved in the fusing-points employed for graduation, and because of the fact that the radiation from platinum does not obey Stefan's law. Furthermore the constants for platinum were found in terms of those of copper oxide, a substance they found, incorrectly, to depart more from a black body than polished platinum. ' Langley and Abbot's Experiments. Langley has de- vised, under the name of bolometer, a radiometric appa- ratus which he has used only incidentally to measure temperatures, but which may be so used and has the advantage over the preceding methods of being more sen- sitive. It consists of a Wheatstone bridge, one arm of which is made of flat wires extremely thin (0.01 mm.) and very short (a few millimeters at the most). The variations of resistance of this arm of the bridge submitted to the radiation are measured. The current passing through the system is capable of raising its temperature 3 or 4; the excess of heat furnished to one of the arms produces a deflection of the galvanometer. The system is fixed at the bottom of a tube which may be pointed like a telescope toward the body whose radia- tion is to be measured; diaphragms fixed at various points stop interior currents of air. One may also, by aid of a lens, concentrate the radiation upon the wire and amplify very much in this way the effect produced w T hen the apparent angle of the object is small. The bolometer of Langley has up to the present been used almost exclusively to study the distribution of radi- ant energy in the solar spectrum, and especially in the infra-red. It is sufficiently sensitive in the hands of 198 HIGH TEMPERATURES. Langley and Abbot to detect changes of less than 0.000001 C. Conditions of Use. We have dwelt at length upon those radiation-pyrometers which have been used up to the present only for a single purpose, the estimation of the sun's temperature, because it is possible that some day or other their usage may penetrate into industrial works, where they may be of real service. In a certain number of industrial operations the temperatures are so high that no substance, not even platinum, can resist for long their action. When it is desired to have apparatus of con- tinuous indications, and at the same time unalterable, it will be necessary to make use of radiation-pyrometers. A tube of fire-clay passing through the lining of the furnace, and penetrating into the midst of the latter for a distance of 0.50 m. to 1.00 m., closed at the inner end and open at the outer, would give a radiating surface at the temperature of the furnace which could be examined by means of a lens projecting upon the measuring apparatus the image of the sealed base of this tube. This arrange- ment also gives radiation obeying very nearly the laws we have discussed, that is, a black body is realized ap- proximately and Stefan's and Wien's laws may be used with radiation instruments. Fery Thermoelectric Telescope. This pyrometer is the only convenient form of instrument making use of total radiation and based on Stefan's law (p. 177) which has come into practical use for temperature-measurements. As in the case of the photometric pyrometers, the limita- tions as to the realization of a black body apply here also. Use is made of the Stefan-Boltzmann law, in the following way: Radiation from an incandescent HEAT-RADIATION PYEOMETER. 199 body is focussed upon a very sensitive thermocouple and raises its temperature. The electromotive force thus generated at the junction actuates a sensitive potential galvanometer in series with the couple in exactly the same way as in the Le Chatelier thermoelectric pyrometer; so that we have here a radiation-pyrometer which is direct- reading by means of a pointer on a scale, and may there- fore readily be made a recording instrument. The difficulty in construction of such an instrument is realizing a material for lens which is transparent for all radiations visible and invisible, so that the pyrometer may be calibrated directly in terms of Stefan's law and so that its indications will be reliable at temperatures however high. This is effected by use of a fluorite lens which for temperatures above 900 C. satisfies the con- ditions of not altering appreciably the radiations trans- mitted through it ; that is to say, the ratio of the radiations absorbed to the radiation transmitted is constant. At low temperatures a large proportion of the energy exists in the form of long wave lengths, and as fluorite has an absorption-band in the infra-red (near 6//), it will absorb a considerable proportion of the radiation, and therefore Stefan's law can no longer be assumed. Fig. 45 illustrates the construction of the instrument, where F is the fluorite lens, P. a rack and pinion for focus- sing the radiations upon the thermo-junction of iron-con- stantan, and protected from extraneous rays by the screens C, D, shown also in section at AB. The thermo-junction is of exceedingly small dimensions, only a few thousandths of a millimeter wide, and is soldered to a silver disk. The leads are brought out to the insulated binding-posts b, b' , so placed as to reduce the chances of extraneous thermal currents to a minimum. The circuit is completed through a sensitive galvanometer provided with a scale. A dia- 200 HIGH TEMPERATURES. HEAT-RADIATION PYROMETER. 201 phragm fixed in size and position, EE, gives an opening of constant angle independent of the focussing whereby the cone of rays striking the junction is not changed hi size by focussing. In making a temperature-measurement it is necessary to sharply focus the image of the incandescent object upon the thermo-j unction by means of the eye-piece 0, and care must be taken that this image is of greater size than the junction. This adjustment once made, the pyrometer functions indefinitely while sighted upon the same object, and readings of the galvanometer scale give temperatures directly from the calibration. The precision attainable with this form of instrument, over the range it may be controlled with the thermoelectric pyrometer, is shown from data obtained by Fery, assum- ing Stefan's law to hold in the form, where E is the total energy of radiation and d the gal- vanometer deflection and T the absolute temperature. , Temp, from Thermocouple. Temp, from Stefan's Law. J in Degrees. Error in %. 11 844 860 + 16 1.85 14 914 925 + 11 *.84 17.7 990 990 .0 21.5 1054 1060 + 6 .60 26.0 1120 1120 .0 32.2 1192 1190 - 2 .17 38.7 1260 -10 .80 45.7 1328 - 8 .60 52.5 1385 - 5 .36 62.2 1458 1450 - 8 .50 It is evident, furthermore, that if the galvanometer has a uniformly graduated scale and the temperature T l cor- responding to any one scale reading ^ is known, that for 202 HIGH TEMPERATURES. any other reading R 2 may be found from the relation which also shows that errors in the galvanometer readings are divided by four when reduced to temperatures. For very high temperatures deflections off the scale of the galvanometer will be obtained. Fery overcomes this diffi- culty by substituting a smaller diaphragm before the objective when the radiation is reduced in the ratio of the areas of the apertures. Shunting the galvanometer will also accomplish the same end, and this latter method is probably capable of more accuracy than Fery's. The highest temperatures which may be estimated by this pyrometer are limited only by the applications of Stefan's law to this extreme region, and whether Stefan's law applies, or not, consistent results, nevertheless, will be obtained. The laboratory form of apparatus described above is not suitable for use in technical practice, and fluorite is difficult to get of sufficient size. An industrial pyrom- eter is readily made by substituting for the fluorite lens one of glass, and for the delicate galvanometer one of the same type and sensibility as used in thermoelectric work; the resulting instrument is robust and sufficiently sen- sitive for all practical uses and as made has a range of from 800 C. to 1600 C., although the upper limit could readily be extended by having two scales on the instru- ment, with a shunt. The indications of the industrial form of this pyrom- eter will not obey Stefan's law, but the instrument may readily be calibrated by direct comparison either with a thermocouple or with a laboratory form of Fery instru- HEAT-RADIATION PYROMETER. 203 ment, and the scale of temperatures engraved on the instrument. Both types of instrument can be use,d to reach lower temperatures (650) by means of more sensitive galvanom- eters. Lower temperatures might also be reached by converting the instrument into a reflecting telescope with a concave mirror behind the thermo-junction, and Fery has just de- signed such an instrument with which temperatures nearly as low as 600 C. may be reached. CHAPTER IX. OPTICAL PYROMETER. Principle. Instead of using the totality of the radiant energy as in the methods described in the preceding chapter, use is made of the luminous radiations only. This utilization may be effected in many different ways, which give methods of unequal precision and varying in facility of manipulation. Before beginning their study, it is well to recall certain properties of radiations. Kirchoff's Law. An incandescent body emits radiations of different wave lengths. For a given wave length and a given temperature the intensity of this emitted radiation is not the same for different bodies: this is expressed by saying that they have for this radiation different emissive powers. Similarly, a body which receives radiations of a given wave length absorbs a part of them and sends back another part by diffusion or reflection; a certain quantity may also traverse the body. The diffusing, reflecting, or transmitting power at a given temperature, for a given wave length, varies from one body to another. The emis- sive power and the diffusive power (in the case of an opaque and non-reflecting body) vary always inversely, resting com- plementary to each other. Substances of great emissive power, as lampblack, have a small diffusive power; substances of small emissive 204 Of THC UNIVERSITY OPTICAL PYROMETER. 205 power, as polished silver, magnesia, have a very great diffusing or reflecting power. If we take as the measure of the emissive power the ratio of the intensity of the radiation of the body consid- ered to that of a black body (p. 173) at the same tempera- ture, and as measure of the diffusive power the ratio of the intensity of the radiation diffused to the incident radiation, the sum of these two quantities is equal to unity. The emissive power of a body varies from one radiation to another, and consequently also its diffusing and trans- mitting powers, since these two powers are complementary to each other. It follows that the relative proportions of the visible radiations received or given off by a body are not the same; so that different bodies, at the same tem- perature, appear to us to be differently colored. At the same temperature, the color proper to a body, and its apparent color when it is lighted by white light, are complementary to each other. Yellow substances, as oxide of zinc heated, emit a greenish-blue light. At tem- peratures less than 2000 the red radiations predominate greatly and mask the inequalities of the radiations of other wave lengths. To render easily visible the colora- tions of radiating bodies it is necessary to compare them with those of a black body under the same temperature conditions. A hole pierced in the body, or a crack across the surface, gives a very good term of comparison to judge of this coloration. \ The intensity of the radiations emitted by a black body increases always with the temperature, and the more rapidly as we approach the blue region of the spectrum; but on the other hand the radiations from the red end are the first to commence to have an intensity appreciable to vision, so that the color of bodies heated to higher and 206 HIGH higher temperatures starts with red, tending towards white passing through orange and yellow. White is, in fact, the color proper to bodies extremely hot, as is the sun. Bodies not black have a law of increase different from that for black bodies, because the emissive power varies with the temperature. It increases unequally for the various radiations, so that the color of bodies, with respect to the color of a black body, changes with the temperature. The following table gives for different colors the ratios of the values of emissive powers of some bodies to that of a black body. The red radiation was observed through a glass containing copper, the green by aid of a chromium copper glass, the blue through an ammoniacal solution of cupric hydrate. The substance covered the junction of a thermoelectric couple, and was cut by grooves; and it was the brightness of the bottom of these grooves which was compared to that of the surface. Red. Green. Blue, 1.0 Acetate of amyl lamp, ) Pigeon-lamp, with mineral oil 1.1 Argand burner, with chimney 1.9 Auer burner 2.05 Fe 3 O melting (1350) 2.25 Palladium melting 4.8 Platinum melting 15. Incandescent lamp 40 Crater of electric arc 10,000 Sun at midday 90,000 Graduation. Le Chatelier made a first graduation of his optical pyrometer by measuring the brightness of iron OPTICAL PYROMETER. 217 oxide heated on the junction of a thermoelectric couple, and admitting that, for the red, the emissive power of this substance is equal to unity.* He found a law of variation of the intensity of the red radiations as function of the temperature, which is well represented by the formula 3210 in which unit intensity corresponds to the most brilliant axial region of the flame of a candle. (T is absolute tem- perature.) The table below gives, for intervals of 100, the intensi- ties of red radiations emitted by bodies of an emissive power equal to unity. These numbers were calculated by means of the interpolation formula give above. Intensities. Temperatures. Intensities. Temperatures. 0.00008 ____ 600 39 ..... 1800 .00073 ____ 700 60 ..... 1900 .0046 ..... 800 93 ..... 2000 .020 ...... 900 1,800 ..... 3000 .078 ...... 1000 9,700 ..... 4000 .24 ....... 1100 28,000 ..... 5000 .64 ....... 1200 56,000 ..... 6000 1.63 ....... 1300 100,000 ..... 7000 3.35 ....... 1400 150,000 ..... 8000 6.7 ........ 1500 224,000 ..... 9000 12.9 ........ 1600 305,000 ..... 10000 22.4 ........ 1700 These results are represented graphically in Fig. 49. After having determined the value of the diaphragm * It has since been shown that the emissive power of iron oxide is less than unity (see p. 178), but this fact does not materially affect the applicability of Le Chatelier's formula as used. 218 HIGH TEMPERATURES. opening c? , which gives equality of brightness of the stand- ard candle with that of the comparison-lamp, and the absorbing power k of the tinted glasses, one may, as was said before, prepare a table which gives directly the tem- perature corresponding to each aperture of the cat's-eye. 5 * 3 ~* 1 it, *! *2 -3 r4 R ^*,~ ^ ,''*' *^^ X t / / / / f / / 7 / / / 2.9 3 3.1 3.3 3.3 3.4- 3.5 3.f> 3.7 3.8 3.'J Log. (2+273J FIG. 49. With an apparatus for which the following table is obtained, in which the plus sign refers to tinted glasses placed before the objective, and the minus sign to those before the comparison-lamp. This graduation applies to all bodies placed in an en- closure at the same temperature, in the interior of fur- OPTICAL PYROMETER. 219 naces for example, and to black bodies whatever the tem- perature surrounding them; for example, it applies very closely for a piece of red-hot iron exposed to the free air. For bodies whose emissive power is inferior to unity, as platinum, magnesia, lime, it is necessary, when they are exposed to the air and not surrounded by an enclosure at the same temperature, to make a special graduation. nperatures. -2 Glasses. -1 Glass. Glass. + 1 Glass. + 2 Glasses. 700 173 800 6.9 23.0 ... 900 11.0 1000 5.6 18.6 1100 10.5 . . 1200 6.5 .... 1300 4.0 13.6 . . . 1400 9.4 . . 1500 . . . . ... 6.6 . . . 1600 ' 4.8 1700 3.6 12.0 1800 9.1 1900 7.3 2000 5.9 Le Chatelier and Boudouard have made a series of measurements on radiations of different wave lengths. The junction of a thermoelectric couple was placed in a small platinum tube, to realize approximately an enclosed space. By taking as unity the brightness of melting platinum, the results obtained are the following for the red, green, and blue radiations: t Log + 273) I r Log/ r I v Log/ r 7 ft Log I b 900 3 .0707 0.0000 4 .95 .00018 4.25 0.00002 5 .3 1180 3 161 .0024 8. 88 ,0087 3.94 .0015 3 .17 1275 3 190 .075 '2 78 037 2.57 .013 a .11 1430 3 230 .23 I 36 16 1.67 .058 a .76 1565 3 265 .72 1 ,86 47 1.20 .24 1 .38 1715 3 300 1.69 23 1, 45 0.16 .9 .95 220 HIGH TEMPERATURES. Evaluation of Temperatures. Finally, Le Chatelier has used his optical pyrometer to determine the very highest temperatures realized in some of the most important phenomena in nature and in the industries. These results, quite different from previous determinations, were at first regarded with considerable reserve; they are admitted to-day as exact, at least within the limits of precision. Here are some of the figures obtained: Siemens-Martin furnace 1490 to 1580 C. Furnace of glass-works 1375 to 1400 Furnace for hard porcelain 1370 " new porcelain 1250 Incandescent lamp 1800 Arc lamp 4100 Sun 7600 This determination of the temperature of the sun, gen- erally believed to be low at the time it was found, has been confirmed by the more recent experiments of Wilson and Gray (p. 194) by a totally different method. Later determinations of the sun's temperature, using the re- cently established laws of radiation (Chapter VII), give values between 5500 and 6500. A series of measurements were made with the same apparatus in iron-works. Here are some results: BLAST-FURNACE SMELTING GRAY PIG. Opening before the tuyere 1930 C, Tapping the pig iron, beginning 1400 " " " end 1520 BESSEMER CONVERTER. Pouring the slag 1580 " " steel into the ladle 1640 " " " " " moulds 1580 Reheating of the ingot 1200 End of the hammering 1080 OPTICAL PYROMETER. 221 SIEMENS-MARTIN FURNACE. Flow of the steel into the ladle, beginning 1580 " " " " " " " end 1420 " hito the moulds 1490 Calibration in Terms of Wien's Law. As approximately monochromatic radiation is used, the Le Chatelier optical pyrometer may be calibrated in terms of Wien's law III (p. 183) by sighting upon a black body (p. 173) whose tem- perature is given by means of a thermocouple. For this purpose Wien's law may be written: log J=.X t +X i i, where J is the intensity of light, in terms of the centre of the Hefner flame for example, and T is the absolute tem- perature. This method of graduation has the advan- tage that only two points are required to completely calibrate the instrument, for the relation between log J and -=- is linear, so that these quantities being plotted give a straight line which may evidently be extended to lower and higher temperatures, since Wien's law has been shown (p. 183) to hold over the widest temperature interval measurable, provided the light used is monochro- matic and the bodies observed approximate blackness and are not luminescent, that is, their light not produced by chemical or electrical excitation. Precision and Sources of Error. We shall give in some de- tail a discussion of the factors which in the use of the Le Chatelier optical pyrometer may influence the photometric settings and so affect the accuracy of temperature deter- minations, as results of such a discussion are illustrative of what may be expected from optical pyrometers in general. The results are taken from those of Waidner 222 HIGH TEMPERATURES. and Burgess, who have made an experimental comparison of all the available optical pyrometers. The sources of error of this instrument may be those due to the standard Hefner amyl-acetate or other stand- ard, the oil comparison-lamp, the focussing system, the nature of the red glass used, and the coefficients of absorp- tion of the glasses used. The first of these affects only comparative results with different instruments, while the others, if they exist, may be of considerable importance in work with a single instrument. We shall consider them in the order named. As only the central portion of the amyl-acetate flame is used, variations in height and fluctuations in total intensity due to various causes such as moisture and carbonic acid in the atmosphere and changes due to differing samples of acetate become almost, if not quite, insignificant in this method of comparison ; so that when using only a small central area of the amyl-acetate flame, it is a very per- fectly reproducible standard under the most varying conditions of burning. Again, the effects of any slight fluctuations in light-intensity are further greatly reduced when transformed into temperature changes as has been shown (p. 171). Thus, the effect of varying the height of the Hefner flame by one millimeter, which amounts to ten per cent of the total intensity when the whole flame is used, causes a change of less than one per cent in the intensity of light from the central area, which is equiva- lent to less than 0.5 C. change in temperature at 1000 C. Although used intermittently as above indicated, the Hefner serves well enough as an ultimate standard by means of which the indications of all photometer-pyrom- eters may be reduced to a common basis, yet the Hefner is not suited for use as comparison-lamp in the pyrometer itself, as has been previously stated. OPTICAL PYROMETER. 223 In a study of the constancy of the comparison-lamp the following arrangement was adopted : In order to ob- tain a perfectly constant source of light with which to compare the flame, a 32 c.p. incandescent electric lamp was placed in a fixed position before the objective of the pyrometer and a glass diffusing screen inserted before the objective. The voltage across the lamp ter- minals was kept rigorously constant thus giving an arbi- trary but invariable standard of illumination. The concordance of results obtained by different ob- servers setting the gasolene flame and observing is shown below: WITHOUT ABSORPTION-GLASS. 1 2 3 4 7.4 7.8 7.6 7.3 7.4 7.9 7.8 7.0 Cat's-eye scale readings. . . 7.2 7.8 7.7 7.8 7.6 7.7 8.0 7.1 7.7 7.7 7.8 8.3 .7.8 7.7 7.4 8.0 Means. 7.55 7.73 7.65 7.60 Observers Nos. 2 and 4 had no experience in the use of the instrument. WITH ABSORPTION-GLASS. Observer 1 3 25.7 25.8 24.0 24.8 23.6 26.0 Cat's-eye scale readings. . . 24.1 25.8 25.4 24.8 24.8 24.9 24.8 25.3 Means... 24.63 25.34 22 4 HIGH TEMPERATURES. Here the greatest variation corresponds to less than three degrees in temperature at 1000 C. To control accurately the flame height in the gasolene lamp, a sight was inserted consisting of a horizontal scratch 2 mm. above the window before the flame, and a very fine platinum wire in the same horizontal plane but in a collar behind the flame. With this improvement an observer can set and control the flame-height to 0.2 mm. Such provision, however, is not necessary except in the most refined work, for experiment showed that for most purposes changes of over 2 mm. may be made in the flame height with unimportant changes resulting in the temperature estimation. Considering the time-effect of burning upon the flame- height and intensity due to local heating and change of depth of oil, it was found that the flame ceases creeping up after ten minutes and will then remain at constant height to within 0.5 mm. until the oil is used up, in three hours, and during all this period the brightness of the flame does not change by an amount corresponding to more than 5 in temperature. It might be expected that oils of different grades would give widely differing results, but an examination of this possible source of error showed that different samples of gasolene and gasolenes mixed with several per cent of a heavy kerosene gave identical results. This is of great importance in the practical use of the instrument as it shows that a calibration made with a given sample of gaso- lene remains good for any other gasolene. From the above it is clear that variations in brightness of the comparison-flame due to all possible causes need not produce errors in temperature measurement of over 5C. at 1000 C., that is within the experimental limits of making the photometric setting, OPTICAL PYROMETER. 225 Considering now the sources of error due to focussing and sighting upon the object whose temperature is sought, it is first to be noticed that there is a minimum distance from the object at which the pyrometer can be focussed, this distance being somewhat over a meter, depending, of course, upon the focal length of the objective and length of draw-tube. There is also a minimum area which can be sighted upon and give an image of sufficient size to completely cover the desired photometric field ; this mini- mum size of object is about 6 mm. on a side when the instrument is at its least distance; for greater distances a larger area must be viewed. The draw-tube can easily be set to 2 mm. when focussing, and as the image is over 20 cm. from the objective in all cases, the resulting error in intensity due to focussing is not greater than 2 per cent. This corresponds to 1 C. in temperature, showing that an error of even 5 mm. in focussing the draw-tube will not produce an appreciable error in temperature estimation. Often, in use, the distance of the instrument from the objects studied needs to be changed considerably, and in rapid work it is not always convenient to- refocus; a change in this distance of a fourth of its value, i.e., from 120 cm. to 150 cm., will produce an apparent change in intensity of only 9 per cent, or about 5 C. in temperature. That these errors of focussing are so small when inter- preted into temperatures, showing that no unusual pre- cautions are needed, is evidently of great convenience in the use of the instrument. The non-monochromatism of the red glass in the eye- piece produces no considerable error in temperature- measurement up to 1600 C., although if this glass is not very nearly monochromatic the differences in hue in the two adjacent photometric fields from the compari- 226 HIGH TEMPERATURES. son-lamp and other sources are very troublesome, and the strain on the eye in matching them is considerable. For the best work at high temperatures a better glass than is usually furnished with the instrument must be used. There remains to be considered the error introduced due to uncertainty in the knowledge of the coefficient of absorp- tion of the absorbing-glasses. If an observation (N f ) is taken with, and then one (N) without, an absorption-glass, we have so that the accuracy in determining k depends directly upon the precision of setting and reading the cat's-eye opening. Errors of over 5 at 1000 C. can hardly occur from this cause, although the determination of k is the most difficult and uncertain of all the operations in opti- cal pyrometry. Modifications of the Le Chatelie'r Pyrometer. For use in technical works and other places where there are sure to be strong drafts of air causing unsteadiness of the flame of the oil comparison -lamp, the Le Chatelier pyrometer might be improved by the substitution of an electric incandescent lamp of low voltage (six) placed before a uniformly ground diffusing-glass screen, which, illumi- nated by the incandescent lamp, becomes the constant comparison source. The electric lamp may be mounted in a vertical arm which serves at the same time as a handle, and then the instrument becomes as portable as an opera-glass. The reliability of such a method of pro- ducing a comparison-light of invariable intensity will be discussed when describing the Wanner instrument. Other modifications will be discussed under the Fery and Warmer pyrometers. OPTICAL PYROMETER. 227 Fe*ry Absorption-pyrometer. This is identical with Le Chatelier's instrument, except that a pair of absorbing- glass wedges p, p' replaces the iris diaphragm, and the 45 "T A f V 1IZZ / \- \ / J Fia. 50. mirror G, with parallel faces, is silvered over a narrow vertical strip, giving a photometric field of form shown 228 HIGH TEMPERATURES. at ab, when looking at a hot crucible. The instrument has a fixed angular aperture, so that no correction has to be made for focussing or for varying distance from furnace. The comparison-light L plays the same role as in Le Chate- lier's pyrometer, and the range of the instrument may be similarly extended by the use of auxiliary absorbing- glasses. Fery has in addition made his instrument mov- able about a horizontal axis, which is a convenience. The calibration is equally simple. If x is the thickness of the wedges, read off on a scale, when the light from the comparison-lamp and furnace is of the same bright- ness, then the relation between brightness / and thickness of wedge is where k is the coefficient of absorption of the glass of the wedges for the red light used and c is a constant. But by Wien's law III (p. 183), assuming it to apply here, B or combining these two equations we have whence Thus it follows that the thickness of the wedge is in- versely proportional to the absolute temperature, so that the calibration may be effected by finding the thickness of wedge for two temperatures only and plotting a straight line and constructing a table giving / and T respectively in terms of x. OPTICAL PYROMETER. 229 It is questionable if there is any gain in substituting the wedge for the cat's-eye in the desire to extend the range over which the instrument may be used without employing the auxiliary absorbing-glasses, for thereby the sensibility is somewhat reduced, and more important still, the wedge instrument cannot be used at such low temperatures as the original Le Chatelier form, nor is there any gain in simplicity of calibration and ease of manipulation. The shape of the photometric field, the use of an aperture of constant angle, and making the instrument movable about a horizontal axis, however, are improvements which may be applied with advantage to the Le Chatelier instrument. Wanner Pyrometer. Description and Calibration. Wanner, making use of the polarizing principle discarded by Le Chatelier, has brought out a photometer-pyrometer which is a modification, suited to temperature-measure- ments, of Konig's spectrophotometer.* The comparison-light is a six-volt incandescent lamp, illuminating a glass-matt surface; monochromatic red light is produced by means of a direct-vision spectroscope and screen cutting out all but a narrow band in the red, and the photometric comparison is made by adjusting to equal brightness both halves of the photometric field by means of a polarizing arrangement. The slit S t is illuminated by light from the comparison source reaching S^ after diffuse reflection from a right- angled prism placed before S v Light from the object whose temperature is sought enters the slit S 2 . The two beams are rendered parallel by the lens L lt and each .dis- persed into a continuous spectrum by the direct-vision prism P. Each of these beams is next separated by a * Konig, Wied. Ann., 53, p. 785, 1894. 230 HIGH TEMPERATURES. \ Rochon prism R into two beams, polar- ized in planes at right angles. Con- sidering only the red light, there would now be four images formed by the lens L 2 , and distributed about the slit 4 . In order to bring two red images oppo- sitely polarized exactly before this slit, a bi-prism B is interposed whose angle is such as to effect this for two images only, at the same time increasing the number of images to eight. There is now in the field of view before the Nicol analyzer, A, two contiguous red fields composed of light oppositely polarized, the light of one coming from S l alone, and of the other from S 2 alone. All the other images are cut off from the slit S 4 . If the analyzer is at an angle of 45 with the plane of polariza- tion of each beam, and if the illumina- tion of S 1 and S 2 is of the same bright- ness, the eye will see a single red field of uniform brightness. If one slit re- ceives more light than the other, one- half of the field will brighten, and the two may be brought to equality again by turning the analyzer carrying a graduated scale, which may be cali- brated hi terms of temperature. If the analyzer is turned through an angle to bring the two halves of the field to the same brightness, the relation between the two intensities from S l and S 2 is OPTICAL PYROMETER. 231 i-tanV- .'-'. () t/2 Since monochromatic light is used, and the comparison- beam and that from the object examined undergo the same optical changes, Wien's law III may form the basis of the calibration. If JQ is the intensity of the light from the standard and J that from the object whose temperature is sought, Wien's law III gives '7 l l \ T~YJ Since the constant C= 14,500 for a black body and ^= 0.656/z as the instrument is usually constructed, a knowl- edge of the apparent black-body temperature of the standard source, together with the reading of the analyzer- scale at the normal point when J=J , for such an instru- ment, is all the data required for its calibration, as any temperature may then be calculated by means of equa- tions (a) and (6) in terms of the scale-readings. This instrument may also of course be empirically calibrated against a thermocouple using a black body to sight upon. It is evidently necessary to be able to always reproduce exactly the standard intensity J . Now the brightness of an electric lamp will vary with the current through it, so it is necessary to check frequently the constancy of illumination of the slit S^ against a standard source of light. An amyl-acetate lamp and a ground-glass diffusing-screen can be placed before the slit S 2 , thus fur- nishing the standard light required. The analyzer is then set at the previously determined normal point and the distance of the electric lamp from S l adjusted or the 232 HIGH TEMPERATURES. current through the lamp changed by a rheostat, until the two fields appear of the same brightness. Sources of Error. A study of a Wanner instrument by Waidner and Burgess has led them to the following FIG. 52. conclusions. The sensibility of this pyrometer varies with change in the angle, and is so adjusted as to be the greatest between 1000 and 1500 C. and is about as follows : . 1 scale div. 1 C. at 1000 C. . 1 scale div. 2 C. at 1500 C. 0, 1 scale div. 7 C. at 1800 C. The reproducibility of the brightness of the amyl-acetate flame as viewed through the ground-glass diffusing- screen is a measure of the ability of the instrument to repeat its indications. It is very important that this diffusing-screen be always placed in exactly the same position relative to the flame and slit S 2 , and further that it be free from dust and finger-marks. These require- ments can only be satisfactorily met by protecting this OPTICAL PYROMETER 233 screen by a cover-glass and providing an adjustment for setting it exactly in place between the flame and slit. The constancy of the amyl-acetate flame as used with this pyrometer under ordinary conditions of burning is illustrated by the following set of observations, during which the current through the electric comparison-lamp was kept rigorously constant by means of a milliamnieter and rheostat: Reading of Instrument. 39.9 39.9 40.1 39.9 39.1 39.2 39.8 39.0 39.6 0.38 This shows that the flame can be relied upon to give an intensity of illumination whose constancy expressed in terms of temperature is 0.5 per cent. Variations in height of the flame, if they do not exceed 2-3 mm., together with fluctuations in atmospheric conditions, will not produce errors in temperature estimation exceeding 1 per cent. The uncertainty of setting the nicol, due to lack of sensitiveness of the eye to exactly match the two halves of the photometric field, is also about 1 per cent, or slightly better with practice. The adjustment of the electric lamp to standard intensity at the point on the scale chosen as normal point can be made, when proper care is taken regarding the diffusing- screen, to 1 per cent expressed in temperature change. 234 HIGH TEMPERATURES. This source of error does not effect relative results in any one series for one setting to the normal point. The "most serious source of error, except when special precautions are taken, is the variation in brightness of the electric comparison-lamp due to variation in the cur- rent furnished by the three-cell storage-battery. With the 10-ampere-hour battery furnished with the Wanner instrument, after making circuit the electro- motive force drops by about 2 per cent in two minutes and then falls off slowly, but nearly recovers the original voltage after remaining on open circuit even for a very short time. When the battery is in good condition the variation in three hours at normal discharge (0.075 ampere) is about 0.08 volt, and somewhat less for the current (0.55 ampere) taken by the lamp; with the battery in poor condition these changes are much accentuated. The following table illustrates the effect of slight varia- tions in current through the lamp on apparent tempera- ture of the amyl-acetate flame, for the small battery of 10 ampere-hours furnished with the instrument. The apparent change in temperature is calculated from the current change: SMALL BATTERY. Time, Minutes. Wanner Scale. Current. Per Cent Change in Current. Apparent Change in Temp. 15 31.2 0.5645 20 31.8 0.5640 0.1 1C. 27 32.7 0.5550 1.7 10 37 34.6 0.5400 4.3 25 3ft 40 Disconnecte 32.5 d battery two 0.5610 minutes. 0.6 3 42 31.7 0.5570 1.5 7 45 32.5 0.5560 2.5 15 47 33.1 0.5505 4.1 24 OPTICAL PYROMETER. 235 A battery of 75 ampere-hours gave similar results. The above results give abundant evidence of the need of maintaining the current through the lamp quite con- stant in work of precision. A series of experiments has shown that in the range 1000- 1500 C. one division on the Wanner scale corresponds to about 0.009 ampere, or 1 C. apparent change in temperature is produced by a fluctua- tion of 0.0012 ampere through the lamp; hence to obtain a precision of 5 the current must be kept constant to 0.01 of its value. The above table shows that this is by no means effected by using the battery without regulating the current, for even with the battery in the best condi- tion the current increases by 2 per cent in the first eight or nine minutes of discharge and then falls off 1 per cent in the next twenty minutes. The temperature coefficient of the battery would produce only insignificant changes. The table shows further that breaking the circuit and then making it again may cause an apparent temperature change of over 20 C. For work of precision, therefore, it is essential to keep the current constant by means of a milliammeter and rheostat, otherwise uncertainties of over 25 C. will occur in the temperature measurements. These will increase with the battery in poor condition. Range and Limitations. The above description of the Wanner pyrometer has shown the great loss of light due to the optical system employed. This prevents measuring temperatures below about 900 C. (1650 F.) with this instrument. There is no method of sighting this pyrom- eter exactly upon the spot desired, except by trial, as no image of the object examined is formed in the eye-piece, but this inconvenience is in part compensated by not having to focus with varying distance from the object. There is another limitation which may in certain cases become a serious source of error; light from incandes- 236 HIGH TEMPERATURES. cent surfaces is in general polarized and, as the Wanner instrument is a polarizing pyrometer, care must be taken to eliminate this source of error when it exists. If an incandescent object is viewed normally the amount of polarized light is very small, but, as the angle of inci- dence increases, the proportion of light polarized becomes greater and greater. Besides varying with the angle of incidence, the amount of polarized light emitted varies widely with different substances, being greatest for polished platinum and very much less for iron, glass, etc. In some measurements made with the Wanner pyrometer on the temperature of an incandescent platinum strip in the neighborhood of 1350 C., Waidner and Burgess have found a maximum difference in the readings of 90 C. for posi- tions of the instrument at right angles to one another in azimuth and for an angle of incidence of 70 with the normal to the surface. This introduces, under these conditions, the possibility of an error of 45 C. in the tem- perature-measurement. This source of error can be eliminated by taking the mean of four readings for azi- muths 90 apart. The magnitude of the error arising from this cause is entirely negligible for all practical pur- poses for many substances, such as iron, porcelain, etc. A review of the sources of error and limitations of the Wanner pyrometer shows that they may exert a rela- tively great effect on the temperature-measurements, and it was, therefore, thought worth while to emphasize them, but on the other hand they may all be practically elimi- nated with reasonable care, and the instrument then be- comes one of great precision and convenience. Holborn and Kurlbaum, and Morse, Pyrometers. If a sufficient current is sent through the filament of an electric lamp the filament glows red at first, and as the current is increased, the filament, getting hotter and OPTICAL PYROMETER. 237 hotter, becomes orange, yellow, and white, just as any progressively heated body. If now this filament is inter- posed between the eye and an incandescent object, the current through the lamp may be adjusted until a portion of the filament is of the same color and brightness as the object. When this occurs this part of the filament becomes invisible against the bright background, and the current then becomes a measure of the temperature as given either by a thermocouple or in terms of the intensity of illumination. Holborn and Kurlbaum Form. A small four- volt electric incandescent lamp L with a horseshoe filament is mounted in the focal plane of the objective and of the eye-piece of a telescope provided with suitable stops D, D, D, and a focussing screw S for the objective. The lamp circuit is completed through a two-cell storage battery B, a rheo- stat, and a milliammeter. Section oilA-0 45 Mirror Absorbing Screen Milli Ammeter The determination of a temperature consists in focus- sing the instrument upon the incandescent object, thus bringing its image into the plane AC, and adjusting the 238 man TEMPERATURES. current by means of the rheostat until the tip of the lamp filament disappears against the bright background, when a previous calibration of current, in terms of temperature for the particular lamp used, gives the temperature by reading the milliammeter. As the temperature of the filament increases, the effect of irradiation or too great brightness becomes blinding, and the photometric comparison is then rendered possible at these temperatures by the introduction of one or more monochromatic red glasses before the eye-piece, giving as well all the advantages of photometry of a single color. Below 800 C. the measurements are more easily made without any red glass, as the filament itself is then red and the lowest temperatures are, of course, reached with the least interposition possible of absorbing media. The lower limit of the instrument is very nearly 600 C. Two red glasses are required for temperatures above 1200 C., and for very high temperatures it is necessary in order to avoid overheating the lamp filament by the current to put absorbing-glasses or a double-prism mirror (Fig. 53) before the objective, and they also, of course, require calibration. At very high temperatures, unless a strictly monochromatic glass is used, the pyrometry becomes difficult, the filament never disappearing completely. The coefficient of absorption of the prism system or of an absorbing-glass may be calculated by making use of Wien's law (p. 183), supposing it to hold for the red glass used. If K is the reciprocal of the coefficient of absorp- tion, T v T 2 the apparent temperatures (absolute) given by the pyrometer, sighting first without and then with the absorbing medium, then Wien's law III gives: , J 1 C log e i \ 1 =! - OPTICAL PYROMETER. 239 where C= 14500 for a black body and X is the wave length for the colored glass used. For very high temperatures, although this formula will give a consistent scale when K has been determined, yet the values obtained are in error by amounts depending upon the monochromatism of the red glass used and the departure of the source from a black body. The eye is particularly sensitive in recognizing equality of brightness of two surfaces, one in front of the other, and this pyrometer, therefore, provides a very delicate means of judging temperatures, since the Iigh1>intensity, as has been shown (p. 171), varies so much faster than does the temperature. The precision attainable with this pyrometer is illus- trated by the following series of observations which are indicative of the ordinary performance of the instrument: Temp, from H-&K. Pyrometer. Temp, from Thermocouple. Temp, from H. &K. Pyrometer. Temp, from Thermocouple. 1347 1347 C. 632 634 C. 1351 1347 634 633 1343 1343 633 633 1333 1342 633 632 1342 1342 Different observers do not differ by any appreciable amount in their readings, and at low temperatures the same values are obtained whether a red glass is used or not. For the calibration of the instrument, it is necessary to find empirically the relation between the current through the lamp and the temperatures for a number of tempera- tures, and then interpolate either analytically, or, better, 240 HIGH TEMPERATURES. graphically. The calibration will evidently be an inde- pendent one for each lamp used. The relation between current and temperature is suffi- ciently well expressed by a quadratic formula of the form C=a+bt+ct*. That this formula gives satisfactory results is shown by observations of Holborn and Kurlbaum for a lamp satisfying the equation CIO 3 = 170.0 +0. 1600* + 0.0001333Z 2 . C amp t obs. t calc. At. 340 686 679 -7C. 375 778 778 402 844 850 +6 477 1026 1032 +6 552 1196 1196 631 1354 1354 712 1504 1504 The question whether or not the temperatures indicated by the lamp will repeat themselves for continued burning or aging is a vital one for the permanence of a calibra- tion and hence for the practical usefulness of the pyrom- eter. Holborn and Kurlbaum as well as Waidner and Burgess have made a thorough study of this possible source of error. Lamps which have not been aged or burned for some tune at a temperature considerably above that at which they will ordinarily be used, undergo marked changes and are unreliable, but, if properly aged, they reach a steady condition, as indicated by the following table of results obtained by Holborn and Kurlbaum on these OPTICAL PYROMETER. 241 lamps. The current is given in each case for a tempera- ture of 1100C. AGING OF LAMPS. Current. Lamp Number 1 After 20 hours burning at 1900 C 0.608 0.592 0.589 " 5 " " " " 613 .592 .592 " 5 " " " " 621 .597 .597 " 5 " " " " 622 .599 .600 " 20 " " " 1500 C 622 .599 .601 If a lamp is not aged its indications may change by as much as 25 C. with time, but after twenty hours' heating at 1800 it will undergo no appreciable further changes over a period of time corresponding to many months if used hi the shop, if not heated above 1500. This state of permanence is sufficient to satisfy the most rigid requirements of practice. Morse Form. This instrument is based on exactly the same principle as the Holborn-Kurlbaum. It will only be necessary in describing it to point out the differences in construction from the German make. Instead of a simple horseshoe filament, Morse uses a large spiral filament in the lamp so that in sighting upon an incandescent body it is necessary to choose some particular spot of the spiral and try to make that spot disappear. This is fatiguing, as the spiral covers a large area and is of just sufficiently varying color to cause the eye to wander. This effect is aggravated by the fact that the instrument is not a telescope, possessing no eye-piece or objective, so that the eye has to accommodate itself back and forth between the filament and the object studied. The four-volt battery for the Holborn-Kurlbaum 242 HIGH TEMPERATURES. lamps is here replaced by a battery of forty or fifty volts to run the spiral lamp, requiring a costly installation. The Morse instrument was designed for use in harden- ing steel, and, throughout the limited temperature range required in this process, in spite of the crudities of con- struction above noted, this pyrometer may be read to about 3 C. within this range. Above 1100 C., however, it is very difficult and soon becomes impossible to make a satisfactory setting. Tests of these spiral-filament lamps show that when aged at 1200 C. they will remain constant for several hundreds of hours within the range over which they are intended to be used. It is interesting in this connection to note the behavior of ordinary incandescent lamps as to permanence. -18 !r~ -n . C.R 50 100 - ^ 200 HOURS 300 400 4? 500" A FIG. 54. Conditions of Use. The optical pyrometer, by reason of the uncertainty of emissive powers and of the relatively slight sensibility of the eye for comparisons of luminous intensities, cannot give as accurate results as the electric methods, although the accuracy attainable, since the sat- isfactory establishment of the laws of radiation throughout practically the attainable temperature range, is sufficient, as we have seen, when proper precautions are taken, for all industrial and most scientific needs. OPTICAL PYROMETER. 243 The optical or radiation-pyrometer is peculiarly well adapted for many cases in which other methods fail, as when contact with the object whose temperature is sought cannot be made or when for any reason the pyrometer must be placed at a distance; for example, in the case of a moving body, as a rail passing into the rolling-mill; in the case of very high temperatures superior to the fusing- point of platinum, as of the crucible of the blast-furnace or that of the electric furnace; in the case of isolated bodies radiating freely into the air, as flames or wires heated by an electric current which cannot be touched without changing their temperature. It is also convenient in the case of strongly heated fur- naces, as steel and porcelain furnaces. But in this usage care must be taken to guard against the brightness of the flames, always hotter than the furnace, and against the entry of cold air. The arrangement with the closed tube described in connection with the heat-radiation pyrometer is indispensable if it is desired to obtain anywhere near exact results. Compared to this last pyrometer, the optical pyrometer has the advantage to require no installation in a fixed position. It has, on the other hand, the incon- venience to require a more active intervention on the part of the operator and can hardly be intrusted to a workman, while the set-up of the heat-radiation pyrometer may be made so that an observation reduces to a reading upon a scale. Temperature of Flames. Any substance inserted in a flame will take up a lower temperature than that of the flame itself, due to conduction, radiation, and diminished speed of the gas-stream around the body. Nichols, by using thermocouples of progressively finer wires, sought to deter- mine true flame temperatures by extrapolating for a wire of zero diameter. The uncertainty of this method is 244 HIGH TEMPERATURES. considerable although it gives consistent results, which are probably low. The radiation methods have been employed by Lum- mer and Pringsheim, Kurlbaum, G. W. Stewart, and Fery. The temperature as given by an optical pyrometer will depend on the thickness and density of the flame as well as upon its reflecting and absorbing powers. The reflecting power of a flame is small and probably varies with the kind of flame; the results as yet obtained are quite dis- cordant on this point. Kurlbaum interposed a flame between a black body and the eye and assumed that the two were of the same temperature when the flame disappeared against its back- ground. This method gave results lower than those obtained by Lummer and Pringsheim (p. 184). Kurlbaum and Stewart both claim that the carbon in the flame departs more widely from a black body than platinum, and the latter gets 2282 for the value of A in Wien's dis- placement equation A m T=A, assuming Nichols's value 1900 C. for the acetylene temperature. Fery has shown, however, that the brightness of the sodium line, measured with a spectrophotometer, is not increased by passing obliquely a beam from an electric light across the flame studied, seeming to indicate that the diffusing power is nil for the light coming from carbon. This would imply a value of A of the order of 2800, or of 2400 C. for the acetylene flame, assuming >1 TO = 1.05. Fery's method of measuring flame temperatures is to produce the reversal of a metallic line by means of light emitted by a solid body brought to the proper temperature. The image of the filament of an incandescent lamp is thrown by a large aperture lens onto the narrow slit of a spectroscope. The rays from the filament pass through the flame to be studied, which contains sodium or other OPTICAL PYROMETER. 245 metallic vapor. When the filament is raised in tempera- ture the D line, say, is ultimately reversed, and at the moment of disappearance the filament and flame are assumed to have the same temperature, which may be measured by sighting an optical pyrometer on the filament. Some of Fery's results are as follows: r Open .......................... 1870C. Bunsen \ Half-open ...................... 1810 IShut ........................... 1710 Acetylene ............................... 2550 Oxyhydrogen with illuminating-gas and ) ^am oxygen .............................. f Oxyhydrogen with H, + O ................ 2420 For this determination, Fery used his absorption-pyrom- eter. The results obtained may be slightly high, but hardly by more than 100 C. , as platinum may be melted in an open Bunsen. All of the above methods assume that flames are non- luminescent, otherwise the results obtained are too high. Absurd results will also be obtained if the flames are color- less, i.e., contain no finely divided particles heated by the flame, as in an open Bunsen. Measurement of the Relative Intensity of Different Radiations. It is on this principle that rests the eye- estimation of temperatures, such as are made by workmen in industrial works. Numerous attempts, none very suc- cessful, have been made to modify this method and make it precise. There is need to consider this only from the point of view of a summary control over the heating of industrial furnaces. a. Use of the Eye. Pouillet made a comparison of the colors of incandescent bodies in terms of the air-thermom- eter. The table that he drew up is reproduced everywhere to-day: 246 HIGH TEMPERATURES. First visible red 525 Dull orange 1100 Dull red 700 Bright orange 1200 Turning to cherry 800 White 1300 Cherry proper 900 Brilliant white 1400 Bright cherry 1000 Dazzling white 1500 The estimation of these hues is very arbitrary and varies from one person to another; more than that, it varies for the same person with the exterior lighting. The hues are different by day from those by night; it is thus that the gas-flame, yellow during the day, appears white at night. It is only in the reds that any accuracy can be had by the eye-method. Workmen can sometimes guess to better than 25 C. up to 800 C. At 1200 errors of over 200 will be made. b. Use of Cobalt Glass. One may exaggerate the changes of hue in suppressing from the spectrum the central radiations, the yellow and green for example, so as only to keep the red and the blue. The relative varia- tions of two hues are the greater the more separated they are in the spectrum; now, the red and the blue form the two extremities of the visible spectrum. It has been proposed for this purpose to use cobalt glass, which cuts out the yellow and green, but lets pass the red and blue. It must be remembered that the ratio of the radiations transmitted varies with the thickness of the glass as well as with their absolute intensities. Let I a and /& be the intensities of the radiations emitted, k a and kj, the proportions transmitted by the glass through a thickness 1. Through a thickness e the proportion transmitted will be which will vary with e in all cases that fc a is different from fc. OPTICAL PYROMETER. 247 It results from this that two cobalt glasses, differing in thickness or in amount of cobalt, will not give the same results. So that if the cobalt glass habitually used is broken, all the training of the eye goes for naught. Besides, cobalt has the inconvenience of having an insuf- ficient absorbing power for the red, which predominates at the more ordinary temperatures that we make use of. It would be possible, without doubt, by the addition of copper oxide, to augment the absorbing power for the red. One would have better and more comparable results by employing solutions of metallic salts or of organic com- pounds suitably chosen. But few trials have been made in this matter. Apparatus of Mesur6 and Nouel. It is known that by placing between two nicols a plate of quartz cut perpen- FIG. 55. dicularly to the axis a certain number of the radiations of the spectrum are suppressed. This latter is then com- posed of dark bands whose spacing depends on the thick- ness of the quartz and the position of the angle of the nicols. Mesure and Nouel have utilized this principle hi order to cut out the central portions of the spectrum; this solution is excellent and preferable to the use of absorb- ing media. The apparatus (Fig. 55) consists essentially of a polarizer P and an analyzer A, whose adjustment to 248 HIGH TEMPERATURES. extinction gives the zero of graduation of the divided circle CC. This circle is graduated in degrees and is movable before a fixed index 7. Between the two nicols P and A is a quartz Q of suitable thickness, carefully cali- brated. The mounting M allows of its quick removal if it is necessary to verify the adjustment of the nicols P and A. The quartz Q is cut perpendicularly to the axis. A lens L views the opposite opening C furnished with a parallel-faced plate glass or, where desired, with a diffusing-glass very slightly ground. The relative proportions of various rays that an incan- descent body emits varying with the temperature, it fol- lows that for a given position of the analyzer A the com- posite tint obtained is different for different temperatures. If the analyzer is turned while a given luminous body is viewed, it is noticed that the variations of colora- tion are much more rapid for a certain position of the analyzer. A very slight rotation changes suddenly the color from red to green. Now, if the analyzer is left fixed, a slight variation in the temperature of the incandescent body produces the same effect. The transmission hue red- green constitutes what is called the sensitive hue. There are then two absorptions, one in the yellow and the other in the violet. This apparatus may be employed in two different ways. First fix permanently the analyzer in a position which gives the sensitive hue for the temperature that is to be watched, and observe the changes of hue which are produced when the temperature varies in one direction or the other from the chosen temperature. This is the ordinary method of use of this instrument. It is desired in a given manu- facturing process (steel, glass) to make sure that the tem- perature of the furnace rests always the same; the instru- ment is adjusted once for all for this temperature. It OPTICAL PYROMETER. 249 suffices to have but a short experience to train the eye to appreciate the direction of the change of hue. The inventors have sought to make of their apparatus a measuring instrument; this idea is quite open to de- bate. In theory this is easy; it suffices, instead of hav- ing the analyzer fixed, to make it turn just to the securing of the sensitive hue and to note the angle which gives the position of the analyzer. But in fact the sensitive hue is not rigorously determinate and varies with the observer. A graduation made by one observer will not hold for another. It is not even certain that the same observer will choose always the same sensitive hue. At each tem- perature the sensitive hue is slightly different, and it is impossible to remember throughout the scale of tempera- tures the hues that were chosen on the day of the gradua- tion. There is even considerable difficulty to recall this for a single temperature. The following figures will give an idea of the differences which may exist between two observers as to the position of the sensitive hue: Sun ...................... 6000 84 86 Gas-flame ................. 1680 65 70 Red-hot platinum ......... 800 40 45 The errors in the estimation of temperatures which result from the uncertainty of the sensitive hue will thus exceed 100. With observers having had more experience the difference will be somewhat reduced, but it will re- main always quite large. Crova's Pyrometer. Crova endeavored to give to the method of estimation of temperatures based on the un- equal variation of different radiations of the spectrum a 250 HIGH TEMPERATURES. scientific precision by measuring the absolute intensity of each of the two radiations utilized ; but this method, from the practical point of view, does not seem to ha ve- given more exact results than the preceding ones. The eye is much less sensitive to difference of intensity than to difference of hue, so that there is no advantage in making use of observations of intensity. Crova compared two radiations, X = 676 (red), ^ = 523 (green), coming from the object studied and from the oil-lamp used as standard. For this purpose, by means of a vari- able diaphragm, he brings to equality one of the two radia- tions emanating from each of the sources, and measures afterwards the ratio of the intensities of the two other radiations. The apparatus is a spectrophotometer. Placed before half the height of the flame is a total reflecting prism, which reflects the light from a ground glass, lighted by the radiations from an oil-lamp, having first passed through two nicols and a diaphragm of variable aperture. On the other half of the slit is projected by means of a lens the image of the body to be studied. Before using the apparatus it is necessary to adjust the extreme limits of the displacement of the spectrum so as to project successively on the slit, in the focus of the eye- piece, the two radiations selected (,1 = 676 and ,1 = 523). For this purpose there is interposed between the two crossed nicols a 4-mm. quartz plate which re-establishes the illuminations; for extinction again, the analyzer must be turned 115 38' for ,1 = 523, and 65 52' for ,1 = 676. The instrument is then so adjusted that the dark band OPTICAL PYROMETER. 251 produced by the quartz is situated in the middle of the ocular slit. The apparatus thus adjusted, in order to make a meas- urement at low temperatures, inferior to those of carbon burning in the standard lamp, one brings to equality the red radiations with the diaphragm, then, without touching the diaphragm again, the green is brought to equality by turning the nicol. The optical degree is given by the formula N= 1000 cos 2 a, denoting by a the angle between the two principal sec- tions of the nicols. For higher temperatures the operation is reversed; one brings first the green to equality by means of the dia- phragm, then the red to equality by a rotation of the analyzer. The optical degree is then given by the formula 1000 N = o , and the rotation varying from to 90. the cos 2 a optical degrees vary from 1000 to infinity. This method, which is theoretically excellent, possesses certain practical disadvantages: 1. Lack of precision of the measurements. In admitting an error of 10 per cent in each one of the observations relative to the red and green radiations, the total possible error is 20 per cent; now, between 700 and 1500 the ratio of intensities varies from 1 to 5: this leads to a difference of & in 800, or 32. 2. Complication and slowness of observations. It is difficult to focus exactly on the body or the point on the body that one wishes to study. The set-up and the tak- ing of observations sometimes require about half an hour. 252 HIGH TEMPERATURES. 3. Absence of comparison in terms of the gas-scale. The a priori reason that had led to the study of this method was the supposition that, in general, the emissive power of substances was the same for all radiations and that consequently its influence would disappear by taking the ratio of the intensities of the two radiations. The measurements of emissive power given previously prove that this hypothesis is the more often inexact. Action of Light on Selenium. It has been known for a long time that light incident upon selenium changes the electric resistance of the latter, and pyrometers based on this principle have been devised. Light from an incan- descent source whose temperature is sought falls upon a selenium cell forming part of an electric circuit in which are a battery and ammeter. As the light varies in inten- sity due to changes in temperature, the resistance of the selenium varies and the indications of the ammeter may be empirically calibrated in terms of temperature. As selenium is quite insensible to the invisible heat-waves, the lower limit of this method is above incandescence. Sele- nium also requires some time to recover its original resist- ance after being acted upon by light, and this lag might prove troublesome. As a dial instrument is used, the method could readily be made recording. CHAPTER X. EXPANSION- AND CONTRACTION-PYROMETERS. Wedgwood's pyrometer, the oldest among such instru- ments, presents to-day hardly more than an historic interest, for its use has been almost entirely abandoned. It utilizes the permanent contraction assumed by clayey matters under the influence of high temperature. This contraction is variable with the chemical nature of the paste, the size of the grains, the compactness of the wet paste, the time of heating, etc. In order to have compa- rable results, it would be necessary to prepare simultane- ously, under the same conditions, a great quantity of cylin- ders, whose calibration would be made in terms of the air-thermometer. Wedgwood employed cylinders of fire- clay, baked until dehydrated, or to 600; this preliminary baking is indispensable, if one wishes to avoid their flying to pieces when suddenly submitted to the action of fire. These cylinders have a plane face on which they rest in the measuring apparatus, so as always to face the same way (see the frontispiece). The contraction is measured by means of a gauge formed by two inclined edges; two similar gauges of 6 inches in length, one an extension of the other, are placed side by side; at one end they have a maximum separation of 0.5 inch, and at the other a mini- mum separation of 0.3 inch. Longitudinally the divisions are of 0.05 inch; each division equals ^J^ of f$ of an inch, 253 254 HIGH TEMPERATURES. or T ^ 7 inch, which corresponds to a relative contraction of T2 i Trg .-i- 1 5- 5 .= g-Ljj. in terms of the initial dimensions. We then have the following relation between the Wedg- wood degrees and the linear contraction per unit of length : Wedgwood 30 60 90 120 150 180 210 240 Contraction 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Le Chatelier has made experiments to determine the degrees of the Wedgwood pyrometer in terms of the scale of the air-thermometer by making use of clayey substances of different kinds, and in the first place of the cylinders from an old Wedgwood pyrometer of the Ecole des Mines. The contraction which accompanies the dehydration is quite variable with the nature of the pastes. In these experiments the time of heating was half an hour. Centigrade temperature 600 800 1000 1200 1400 1550 Wedgwood 4 15 36 90 132 Argile de Mussidan 2 14 36 78 120 Limoges porcelain 2 21 88 91 Faience de Choisy-le-Roi. ... 02 5 12 48 75 Faience de Nevers 32 Melted Melted Kaolin 4 12 15 55 118 Clay... ....... 25) 4 9 19 123 160 Titanic acid. . . 75 ) This table shows how variable are the observations; it is impossible, consequently, to compare the old measure- ments of Wedgwood and of his successors, because the manufacture of the cylinders has varied with the course of time. Wedgwood had given a graduation made by a process of extrapolation which he has not explained, a graduation according to which he attributed 10,000 centigrade to 130 of his pyrometer, which corresponds to about 1550. One might still seek to re-establish the graduation by utilizing the determinations of the fusing-points of the EXPANSION- AND CONTRACTION-PYROMETERS. 255 metals made by Wedgwood, but the results are too dis- cordant to warrant any definite conclusion. According to Wedgwood, copper would be more fusible than silver, iron would not be far removed from silver; it is probable that these observations were made with very impure metals, or at any rate were made with metals much oxidized before their fusion. In any case the cylinders which he made use of in his first experiments assume a much greater con- traction than those of the pyrometer of the School of Mines whose graduation was given above. One might with considerable reserve indicate'the following graduation for measurements made with the first cylinders employed about 1780: Wedgwood degrees 15 30 100 140 Centigrade degrees 600 800 1000 1200 1400 The preparation of the cylinders was a most care-taking operation. Moulded in soft paste they were necessarily somewhat irregular. After the first baking they had to be trimmed to bring them to a uniform size. To-day, in several pottery works where the method is still employed, a much greater regularity is obtained by using a very dry paste, 5 per cent, of water for example, moulding it under great pressure, about 100 kg. per square centimeter, in moulds of turned steel. The precision of the measurements is increased by augumenting the diameter, to 50 mm. for example. It is necessary at the same time to reduce the thickness to about 5 mm., in order that the compression be uniform throughout the mass. This apparatus cannot be recommended in any instance as a true pyrometer, serving indirectly to evaluate tempera- tures in terms of the air-thermometer scale. The gradua- tion is laborious and can only be made by means of the intermediary of another pyrometer; the use of fixed points 256 HIGH TEMPERATURES. is not adapted for this graduation because the curve of contraction of clay in function of the temperature is too irregular for two or three points to determine it; in no case do the indications of this instrument possess any con- siderable precision. But as simple pyroscope, that is to say, as an apparatus to indicate merely the equality or inequality of two tem- peratures, the Wedgwood pyrometer is very convenient. It has the advantage of costing almost nothing and it is easy to use and within the comprehension of any workman. It seems to be particularly recommendable for certain ceramic industries, in which the ordinary pastes found there .may be used to make the contraction-cylinders. It is neces- sary for this that the normal baking of these pastes is stopped at a temperature comprised within the period of rapid contraction. This is the case with fine faience and with ordinary earthenware. I That would not be the case, how- ever, for stannife ous faience nor for porcelain, because the baking of the first is stopped before the beginning of the contraction, and that of the second after its finish. Expansion of Solids. Some of p IG 56. the earliest forms of indicating- pyrometers were based on the relative expansion of two metals, or of a metal and graphite or fire-clay. Some of these instruments have had and still EXPANSION- AND CONTRACTION-PYROMETERS. 257 enjoy a very wide use both in Europe and America, and some of them are suitable for certain industrial processes not requiring exact temperature determination or control, as air-blasts. A common form of dial instrument is shown in Fig. 56. A tube of iron encloses a rod of graphite, and their differential expansion with change in tempera- ture is communicated by levers to a pointer turning over a dial graduated in degrees. The upper limit of these instruments is about 800 C. (1500 F.), but they deteriorate rapidly when used at the higher temperatures. Their indications change with time due to changes produced in the materials by continued heatings. Correcting the zero of such an instrument, which should be done frequently, does not completely correct the rest of the scale, as the expansion properties of the two materials change differently with heating. Varying depths of im- mersion will also change the readings. The Joly Meldometer. A modified form of this instru- ment was previously mentioned, p. 195. As in its usual form, it may be of great service to chemists, metallurgists, and others in determining the melting-points and identifi- cation of minute specimens of minerals, salts, metals, and alloys, a further description may be of interest. A platinum strip (Fig. 57) 10 cm. long, 4 mm. wide, and 0.02 mm. thick, is held between two clamps C, C, and kept under a slight tension by the spring s. A storage-battery current controlled by a small step rheostat R is sent through the platinum strip whose length at any instant is given by the micrometer screw M , whose contact is made appreciable by the closing of the circuit (f an electric bell. The platinum strip is calibrated preferably by means of salts of known melting-points, as KNO 3 (399 C.), KBr (723), and K 2 SO 4 (1071). Metals may also be used, but they tend to deteriorate 258 HIGH TEMPERATURES. the platinum. The upper limit of the instrument is about 1500 C., the Pd point being obtainable. Per- manent elongation sets in somewhat before this point is reached. The gold-point (1065 C.) can easily be de- termined to better than 2 C., and only a few moments are required for an observation. EXPANSION- AND CONTRACTION-PYROMETERS. 259 To take an observation, a speck of the specimen whose melting-point is sought is placed on the middle of the strip under a low-power microscope magnifying about twenty-five times. The current is increased and at the instant of melting, as observed with the microscope, the micrometer is set to make contact and read, when by interpolation, most conveniently made graphically, the temperature is found corresponding to the length of strip observed. This instrument gives a nearly but not quite linear relation between length of strip and temperature. High-range Thermometers. Although mercury boils normally at about 356 C., yet this liquid subjected to high pressure may be kept from boiling and, suitably enclosed, may be used as thermometric substance to much higher temperatures. Compressed under an atmos- phere of some inert gas, as nitrogen or carbonic acid, and enclosed in a very hard glass, as Jena 59 ra , a borosilicate glass, the mercury-thermometer can be used up to 550 C. (1000 F.). The bulbs of such thermometers should be carefully annealed, before filling, at a temperature higher than the instrument is to be used, and the thermometer should also be annealed after it is made and allowed to cool slowly, otherwise considerable and irregular changes in its indications will occur, amounting to several degrees. The zero reading of such a thermometer should be taken after every observation in work of precision. If a con- siderable length of stem emerges into the ah* when taking a reading, a very considerable error, 25 C. or so, may be introduced at high temperatures due to the difference in temperature of the bulb and stem. This " stem correction" is very nearly: Stem correction =0.00016 -n-(T-t)C., 260 HIGH TEMPERATURES. where n = number of degrees emergent from bath; T = temperature of bath; Z = mean temperature of the emergent mercury column determined by some auxiliary means, as the faden-ther mo meter of Mahlke.* The glass of mercury-thermometers has been success- fully replaced by quartz, which is almost an ideal ther- mometric envelope, possessing an insignificant expansion and no appreciable zero lag, and capable of being: used at very high temperatures. Such mercury-in-quartz thermom- eters are now constructed by Siebert and Kiihn, and are graduated to about 700 C. Dufour has tried to substitute tin for mercury-in-quartz thermometers, thereby attaining a temperature of over 1000 C. Such thermometers have not yet, however, come into use. It is a difficult matter not yet satisfactorily solved to find a substance suitable to use as thermo- metric fluid in quartz at high temperatures. * Mahlke, Zeitsch. /. Instru'k., p. 58, 1893. CHAPTER XI. FUSING-POINT, DILUTION-, AND TRANSPIRATION- PYROMETERS. Fusing-point Pyrometry. A long time ago it was pro- posed to compare temperatures by means of the fusing- points of certain metals and alloys. But the non-oxidiz- able metals are not numerous and all are relatively very costly: silver, gold, palladium, platinum. Use has, however, been made sometimes of these metals and their alloys, in admitting that the fusirig-point of a mixture of two substances is the arithmetical mean of the points of fusion of the components, which is not quite exact. The use of these alloys is entirely abandoned to-day, and with reason. By making use of metallic salts, among which a great number may be heated without alteration, one might con- stitute a scale of fusing-points whose employ would be often very convenient; but this work is not yet done, at least not in a sufficiently precise manner. To the separate salts may be added their definite combinations and their eutectic mixtures which have perfectly definite fusing- points. But one cannot take any mixture whatever of two salts, because in general the solidification takes place throughout a large interval of temperature and in a pro- gressive manner. 261 262 HIGH TEMPERATURES. Instead of utilizing the fusion of crystallized substances which pass abruptly from the solid to the liquid state, use may be made of the progressive softening of vitreous matters, that is to say, of mixtures containing an excess of one of the three acids, silicic, boric, or phosphoric. It is necessary in this case to have a definite process for defining a type degree of softening; a definite depression of a prism of given size is taken. These small prisms, formed of vitreous matters, are known under the name of fusible cones. This method was first devised by Lauth and Vogt, who applied it in the manufactures at Sevres before 1882. But they did not develop it as far as was possible; they were content to construct a small number of fusible cones corresponding to the various temperatures employed in the manufacture of the Sevres porcelain. Seger's Fusible Cones. Seger, director of a research laboratory at the royal pottery works of Berlin, published, in 1886, an important memoir on this question. He deter- mined a whole series of fusible cones of intervals of about 25, including the interval of temperature from 600 to 1800. The substances which enter into the composition of these cones are essentially: Pure quartz sand; Norwegian feldspar ; Pure carbonate of lime; ^ Zettlitz kaolin. The composition of this last is* SiO 2 46.9 A1 2 O 3 38.6 FeO 3 0.8 Alkalies 1.1 Water.., .12.7 FUSING-POINT PYROMETERS. 263 In order to obtain very infusible cones, calcined alumina is added, and for very fusible cones oxide of iron, oxide of lead, carbonate of soda, and boric acid. The shape of these cones (Fig. 58) is that of triangular pyramids of 15 mm. on a side and 50 mm. high. Under the action of heat, when softening begins, they at first contract without change of form, then they tip, bending over, letting their apex turn downwards, and finally flatten- FIG. 58. ing out completely. One says that the cone has fallen, or that it has melted, when it is bent half-way over, the point directed downwards. The fusing-points of these substances have been deter- mined at the Berlin porcelain works by comparison with the Le Chatelier thermoelectric pyrometer, previously de- scribed. The cones are numbered, for the less fusible, which were first adjusted, from 1 to 38; this latter, the least fusible, corresponds to 1980. The second series, more fusible, and established later, is numbered from 01 to 022; this last cone, the most fusible, corresponds to 590. If, instead of using the cones of German make, one wishes to make them himself in employing the same formulae, it is prudent to make a new graduation. The 264 HIGH TEMPERATURES. kaolins and feldspars from different sources never have exactly the same compositions, and very slight variations in their amounts of contained alkali may cause marked changes in the fusibility, at least for the less fusible cones. It is to be noticed that in a great number of cones silica and alumina are found in the proportions A1 2 O 3 + 10SiO 2 . This is for the reason that this mixture is more fusible than can be had with silica and alumina alone. It is the starting-point to obtain the other cones, the less fusible by the addition of alumina, and the more fusible by the addition of alkaline bases. The table on pages 266 and 267 gives the list of cones of Seger's scale. These cones may be classed in a series of groups in each of which the compositions of different cones are derived from that of one of them, generally the most fusible, by addition in varying proportions or sometimes by substitu- tion of another substance. The cones 28 to 38 are derived from the cone 27 by the addition of increasing quantities of A1 2 O 3 . The cones 5 to 28 from the cone 5 by addition of in- creasing quantities of the mixture Al 2 3 +10Si0 2 . The cones 1 to 5 from the cone 1 by substitution of increasing quantities of alumina for the sesquioxide of iron. The cones 010 to 1 from the cone 1 by the substitution of boric acid for silica. The cones 022 to Oil from the cone 022 by the addition of increasing quantities of the mixture Al 2 O 3 -f 2SiO 2 . Fig. 59 gives the graphical representation of these data; the ordinates are temperatures, and the abscissae are values of x from the table. These fusible cones of Seger are pretty generally used in the ceramic industry; they are very convenient in all FUSING-POINT PYROMETERS. 265 intermittent furnaces whose temperature has to increase constantly up to a certain maximum, at- which point the coohng-off is allowed to commence. It is sufficient, before firing up, to place a certain number of fusible cones oppo- site a draft-hole closed by a glass, through which they may 2000* SSfflffl FIG. 59. be watched. In seeing them fall successively, one knows at what moments the furnace takes on a series of definite temperatures. In continuous furnaces, the cones may be put into the furnace during the process, but that is more delicate. It 266 HIGH TEMPERATURES. is necessary to place them on little earthenware supports that are moved into the desired part of the furnace by an iron rod. When, on the contrary, they are put in place at the start in the cold furnace, they are held in place by a small lump of clay. Deg. Nos. T. Composition. X Formulas. 38 1890 1A1 2 O 2 +1 SiO 2 9 36 1850 + 1.5 ' 8 35 1830 + 2 ' 34 1810 + 2.5 ' 33 32 31 30 1790 1770 1750 1730 + 3 ' + 4 ' + 5 * + 6 ' X A1 2 3 + (1-X)(A1 2 3 + 10 SiO 2 ) 29 1710 + 8 " 28 1690 1 +10 " , 27 1670 1 -j JJ-3 gjO [ +20(A1 2 3 + 10 Si0 2 ) 26 1650 1 ' " +7.2 93 25 1630 1 " +6.6 24 1610 + 6 23 1590 + 5.4 22 1570 + 4.9 21 1550 + 4.4 20 1530 + 3.9 19 1510 + 3.5 18 1490 + 3.1 X(A1 2 3 +10 SiO 2 ) 17 1470 + 2.7 4-fl xi^'^ 2 *-H 16 1450 + 2.4 79 \0.7 CaO ' 15 14 1430 1410 + 2.1 + 1.8 + 0.5(Al 2 O 3 +10 SiO 2 )) 13 1390 + 1.6 12 1370 + 1.4 11 1350 + 1.2 58 10 1330 + 1 9 1310 + 0.9 8 1290 + 0.8 7 1270 + 0.7 6 1250 + 0.6 5 1230 1 " +0.5 4 1210 1 " +0.5 Al 2 O 3 + 4SiO 2 1 3 1190 1 _i_ J 0.45 A1 2 O 3 I ,1 Q'O < 0.05 Fe 2 O 3 1 X (0.5Al 2 O 3 + 4 SiO 2 ) 2 1170 1 " +|{J;J Fe^ 3 l +4Si 2 + (l-X).(0.5Fe 2 O + 4SiO 2 + 0.7CaO) 1 1150 1 0.2 Fe 2 O 3 ' FUSING-POINT PYROMETERS. 267 Nos. Deg. Composition. X Formula. 01 02 1130 1110 , (0.3K 2 0) 1 "(0.7CaOf 1 <0.3A1 2 3 ) t (0.2Fe 2 3 f + + " + ( 3.95 SiO 2 j 3.90 SiO 2 3 1.05 03 1090 1 + " + J 3.S5 SiO 2 04 1070 1 + " + j 3^80 SiO 2 1 0.20 BaOg X SiO 05 1050 1 + 1 " + t 3.75 SiO 2 1 0.25 B-jOg 1.25 10 06 1030 1 + 1 " + J 3.70 Si0 2 1 0.30 B2O 3 Vr B (D *d F! c*- O CO M ^ a.*o 00 ffi CD S ? 2" 1 ^ O^ Oi H"* *vj *1 vli ^ 2. S s- 3 ^* o 3 O O <=><> to O5 Ci ^ CO CO tO tO GC Oi O Cn rf- IO i ' tO K> Oi CO O i-* O Cn Cn COCOMOCO*-' O ^ l- -080 ?s . ^ OD* ^ .of O C2 ^ ? 8- Oi MM en CnO~4 O ^ss is Recording Thermocouple S 1 ' t i H- l OOOCOCO ~ ~ -C iC OOO5OiO5C?i Cn COh-toto ^^rfxiCn M ODO5t-' O t-'OOCn CiO?Oidbon. Phil. Mag. (5\ 44 (1897), p. 445; 45 (1898), p. 525. Wade. Wied. Beibl., 23 (1S99), p. 963; Proc. Cainbr. Soc., 9 (1898), p. 526. Waidner and MaUory. Phys. Rev., S, p. 193 (1S99). Barnes and Mclntosh. New form of platinum thermometer. Phil. Mag., 6 (1903), p. 353. BIBLIOGRAPHY. 323 Whipple. Temperature indicator, etc. Phys. 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Saladin Iron and Steel Metall. and Metallog., Jan. 1904. 332 BIBLIOGRAPHY. FUSING- AND BOILING-POINTS. FUSION. Prinsep.Airn. Chim. et Phys., 2d Series, 41 (1829), p. 247. Lauth. Bull. Soc. Chim. Paris, 46 (1886), p. 786. E. Becq-uerel.Aim. Chim. et Phys., 3d Series, 68 (1863), p. 497. Violle.C. R., 85 (1877), p. 543; 87 (1878), p. 981; 89 (1879), p. 702. Holborn and Wien.Wied. Ann., 47 (1892), p. 107; 56 (1895), p. 360; also Zeits. fur Instrumentenk. (1892), p. 257. Holborn and Day. Drude's Ann., 4, 1 (1901), p. 99, and Am. Jour. of Sci., 11 (1901), p. 145. Wied. Ann., 68 (1899), p. 817, and Am. Jour, of Sci. (4), 8 (1899), p. 165. Ehrhardt and Schertel. Jahrb. fur das Berg- und Hiittenw. im K. Sachseri (1879), p. 154. Ledeboer. Wied. Beib., 5 (1881), p. 650. Van der Weyde.1879, see Carnelly's Tables. Calkndar. Phil. Mag., 5th Series, 47 (1899), p. 191; 48, p. 519. Curie. Ann. de Chim. et de Phys., 5th Series, 5 (1895). Barus. Bull. 54, U. S. Geological Survey (1889), and Behandlung u. Messung hoher Temp. Leipzig (1892); Am. Jour, of Sci., 3d Series, 48 (1894)., p. 332. Berthelot.C. R., 126, Feb. 1898. Le Chatelier.C. R., 114 (1892), p. 470. V. Meyer, Riddle and Lamb. Chem. Ber., 27 (1894), p. 3129. (Salts.) MoUenke. Zeits. fur Instrumentenk., 19 (1898), p. 153. (Iron and Steel.) Cusack. Proc. Roy. Irish Acad., 3d Series, 4 (1899), p. 399. Landolt and Bbrnstein. Phys. Chem. Tabellen, Berlin, 1894. Carnelly. Melting and Boiling Point Tables, London, 1885. Holman, Lawrence and Barr. Phil. Mag. (5), 42 (1896), p. 37, and Proc. Am. Acad., 31, p. 218. Heycock and Neville. Phil. Trans., 189, p. 25; Jour. Chem. Soc., 71 (1897), p. 333; Nature, 55 (1897), p. 502; Chem. News, 75 (1897), p. 160. Heraeus Manganese. Zs. Elecktroch., 8 (1902), p. 185. Nernst.Zs. Elektrotech., 1903. Rasch. Ann. d. Phys., 1904. BIBLIOGRAPHY. 333 D. Berthelot. Ann. Chim. et Phys., 1902. Gold. C. R., 138 (1904), p. 1153. Richards. Application of phase rule to Cu, Ag, Au. Am. Jl. ScL (4), 13 (1902), p. 377. Jacquerod and Perrot.Gold. C. R., 138 (1904), p. 1032. EBULLITION. Barus. L. C. (under Fusion), and Am. Jour. (5), 48 (1894), p. 332. Troost. C. R., 94 (1882), p. 788; 94 (1882), p. 1508; 95 (1882), p. 30. Le Chatelier. C. R., 121 (1895), p. 323. (See also under Thermo- electric Pyrometer.) Berthelot. Seances de la soc. de physique, Paris, Feb. 1898, and Bull, du Museum, No. 6 (1898), p. 301. Callendar and Griffiths. Proc. Roy. Soc. London, 49 (1891), p. 56. Chappuis and Harker. Travaux et Me*m. du Bureau Int. des Poids et des Mesures, 12, 1900; Phil. Trans., 1900. Preyer and V. Meyer. Zeits. fur Anorg. Chem., 2 (1892), p. 1; Berl. Ber., 25(1892), p. 622. S. Young. Trans. Chem. Soc. (1891), p. 629. MacCrae. Wied. Ann., 55 (1895), p. 95. Callendar. Phil. Mag. (5), 48 (1899), p. 519. (Fusion also.) D. Berthelot. Ann. Chim. et Phys., 1902. Fery. Cu and Zn. Ann. Chun, et Phys. (7), 28 (1903), p. 428. R. Rothe Sulphur. Zs. Instrumk., 23, p. 364 (1903). PYROMETRIC MATERIALS. PORCELAIN I EXPANSION. Deville and Troost. C. R., 57 (1863), p. 867. Bedford ft. A. Report, 1899. Benoit. Trav. etMem. du Bureau Int., 6, p. 190. Tutton. Phil. Mag. (6), 3 (1902), p. 631. Chappuis. Phil. Mag. (6), 3 (1902), p. 243. HoWorn and Day. Aim. der Phys. (4), 2 (1900), p. 505. Holborn and Gruniesen. Ann. der Phys. (4), 6 (1901), p. 136. 334 BIBLIOGRAPHY. METALS: EXPANSION. Holborn and Day. Ann. der Phys., 4 (1901), p. 104; Am. Jl. Sci. (4), 11 (1901), p. 374. Le Chatelier.C. R., 128 (1899), p. 1444; 129, p. 331; 107 (1888), p. 862; 108 (1896), p. 1046; 111 (1890), p. 123. Charpy and Grenet.C. R., 134 (1902), p. 540. Terneden. Thesis, Rotterdam, 1901 (Fortsch. der Phys., 1901). Dittenberger.Zs. Ver. Deutsche Ingen., 46 (1902), p. 1532. QUARTZ. Le Chatelier.C. R., 107 (1888), p. 862; 108, p. 1046; 130, p. 1703. Callendar. Chem. News, 83 (1901), p. 151. Holborn and Henning. Ann. der Phys., 4 (1903), p. 446. Scheel Deutsch. Phys. Ges. (5), 5 (1903), p. 119. Verh. Phys. Tech. Reichsanstalt, 1904. Shenstone. Properties of Amorphous Quartz. Nature, 64 (1901), pp. 65 and 126, contains history to date. Dufour. Tin-quartz thermometer. C. R., 130, p. 775. Villard. Permeability for H at 1000 C. C. R., 130, p. 1752. Joly. Plasticity, etc. Nature, 64 (1901), p. 102. Moissan and Siemens. Action of water on. C. R., 138 (1904), p. 939. Solubility in Zn and Pb. C. R., 138 (1904), p. 86. Vapor pressure of. C. R., 138 (1904), p. 243. Heraeus. Properties: a general summary. Zs. Elektroch., 9 (1903), p. 848. Brun. Fusion. Arch. Sc. Phys. Nat. (Geneva) (4), 13 (1902), p. 313. Hititon. Lamps, etc. Am. Electroch. Soc., Sept. 1903. GLASS: EXPANSION. Holborn and Gruniesen. Ann. der Phys. (4), 6 (1901), p. 136. Bottomley and Evans. Phil. Mag., 1 (1901), p. 125. VARIOUS SUBJECTS. Le Chatelier. Specific heat of carbon. C. R., 116 (1893), p. 1051; Soc. Franc, de Phys., No. 107 (1898), p. 3. Barus. Bull, of U. S. Geological Survey No. 54, 1889. (Pyrom- etry.) Report on the progress of pyrometry to the Paris Con- BIBLIOGRAPHY. 335 gress, 1900. (This is the latest and best summary of pyrometric methods to date.) Viscosity and temperature. Wied. Ann., 96 (1899), p. 358; and Callmdar, Nature, 49 (1899), p. 494. Long-range temperature and pressure variables in physics. Nature, 56 (1897), p. 528. Baly and Chorley. Liquid-expansion pyrometer. Berl. Ber., 27 (1894), p. 470. Dufour. Tin in quartz-pyrometer. C. R., 180 (1900) , p. 775. Berihelot. Interference method of high-temperature measurements. C. R., 120 (1895), p. 831; Jour, de Phys. (3), 4 (1895), p. 357; C. R., Jan. 1898; applications in C. R., Feb. 1898. Moissan. Le four electrique, Paris, 1898. Also in English. Fliegner. Specific heat of gases. Wied. Beibl., 23 (1899), p. 964. Topler. Pressure-level apparatus. Wied. Ann., 56 (1895), p. 609; 57 (1896), p. 311. Quincke. An acoustic thermometer for high and low temperatures. Wied. Ann., 63 (1897), p. 66. K. Scheel Ueber Fernthermometer. Veriag v. C. Marhold, Halle, 1898. 48 pp. Heitmann. Ueber einen neuen Temperatur-Fernmessapparat von Hartmann und Braun. E. T. Z., 19 (1898), p. 355. Chree Recent work in thermometry. Nature, 58 (1898), p. 304. Lemeray. On a relation between the dilation and the fusing-pointe of simple metals. C. R., 131 (1900), p. 1291. Holborn and Austin. Disintegration of the platinum metals hi different gases. Phil. Mag. (6), 7 (1904), p. 388. Stewart. (Same as preceding.) Phil. Mag. (5), 48 (1899), p. 481. Hagen and Rubens. On some relations between optical and electrical properties of metals. Phil. Mag. (6), 7 (1904), p. 157. KahJbaum. On the distillation of metals. Phys. Zs. (1900), p. 32. Kahlbaum, Roth, and Seidter. (Ibid.) Zs. Anorg. Ch., 29 (1902), p. 177. j HOT-BLAST PYROMETERS. (From Sir Roberts-Austen's Metallurgy.) J. Iron and Steel Inst., (1884) pp. 195, 240; (1885) p. 235; (1886) p. 207; (1888), 2, p. 110. Proc. Inst. M. E. (1852), p. 53. Jl. Soc. Chem. Ind., (1885) p. 40; (1897) p. 16. Wiborgh Industrial Air Pyrometer. Jl. Ir. and St. Inst., 2 (1888), p. 110. 336 Callendar. Industrial Air Pyrometer. Proc. Roy. Soc., 50 p. 247. Measurement of extreme temperatures. Nature, 59, pp. 495 and 519 a review of various pyrometric methods. Siebert.Quntz Thermometers. Z*. Elekiroch. (Halle), 10, p. 26. Mahlke. On a comparison apparatus for thermometers between 250 and 600 C. Zs. Instr.kunde, 14 (If 94), p. 73. F. Kraft. Evaporation and boiling of metals in quartz in electric furnace. Ber. Deut. Ch. Ges., 36, p. 1690 (1903). CHEMICAL DETERMINATIONS OF TEMPERATURES. Haber and Richardt.The water-gas equilibrium in the Bunsen flame, and the chemical determination of high temperatures. Zs. Anorg. Cheni., 38 (1904), p. 5. Zenghelis. Chemical reactions at very high temperatures. Zs. Phys. Chem., 4G (1903), p. 287. Nemst. On the determination of high temperatures. Phys. Zs., 4 (1903), p. 733. RESISTANCE FURNACES. A. Kaldhne. On electric resistance furnaces. Ann. d. Phys., 11, p. 257 (1903). E. Haagen. Platinum-foil furnaces. .Zs. Elektroch., p. 509 (1902). W. C. Heraeus. Electrical laboratory furnace. Zs. Elektroch., p. 201 (1902). C. L. Norton. Laboratory electric furnaces. Elec. World and Eng., 36, p. 951 (1900). F. A. J. Fitzgerald. Principles of resistance furnaces. Trans. Am. Elec.chem. Soc., 4, p. 9; Elec.chem. Indus., 2, p. 242, 1904. D. Berthelot.-A.un. Phys. et Chim. (1902, I.e.). Holborn and Day. Ann. der Phys. (1901, 1. c.). Doelter. Two electric furnaces for melting-points. Centralbl. f. Min. (1902), p. 426. INDEX. Abbot, 197, 198 Actinometer, 190 Aging of lamp*, 241, 242 Air-thermometer, 16, 17, 24, 31, 36, 56, 103 normal thermometer, 36 Aluminum, freezing-point, 306 Aniline, boiling-point, 307 Antimony, freezing-point, 305 Arnold, 167 Avenarius, 121, 153 Barr, 163 Barus, 7, 53, 80, 155, 157, 269, 29^, 315 gas-pyrometer, 75 thermoelectric pyrometer, ITS, 134, 15S Beckmann, 1^3 Bevjuerel, 16, 50, 51, 64, 135, 20^, 29S, 299, 300 gas-pyrometer, 69 thermoelectric pyrometer, 120, 121 Bedford, 53 Bell, Sir Lothian, 291 Benoit, 51 Benzophenone, boiling-point, 307 Berthelot, 94 D. Berthelot, 8, ?5, 33, 34, 164, 298, 299, 300 interference gas-pyrometer, 86, 314, 315 Biju-Duval, 93, 97 Black body, 173, 176, 231, 315 Bolometer, 197, 276 Boltzmann, 178, 182, 199, 313 Boudouard, 219 Boys, 194 Brit. Assoc. Rpt. on platinum- thermometry, 102 Bureau, International, 20, 22, 26, 36, 110 Bureau of Standards, 309 Calendar, 7, 26, 29, 31, 32, 34, 35, 42, 110, 114, 269, 296, 29\315 electric- resistance pyrometer, 102, 104, 105, 106;il2, 273, 276, 277 gas-thermometer, 42 Calorimeters, 94 Berthelot, 94 jacketed, 95 Siemens, 97 Calorimetric pyrometer, 9, 91 calorimeters', 94 choice of metal, 92 conditions of use, 99 precision of, 97 Carnetty and Burton, 268 Cell, standard, 128 West on, 129 Carhart-Clark, 129 Chappuis, 20, 21, 22, 24, 26, 31, 32, 34, 40, 45, 50, 53, 54, 110, 296 Charpy, 167, 284, 285 Cobalt glass, use of, 246 Compeaux, 52 337 838 INDEX. Conclusion, 312 Contraction-pyrometer, 11, 253 Copper, freezing-point of, 301, 304 Cornu, 210 Corrections to: constant-pressure thermome- ter, 62 constant -volume thermome- ter, 56 voluminometer thermometer, 64 Crafts, 7, 23, 52, 61, 63, 82, 86, 113, 296 Crova, 186 pyrometer of, 249 Day, 8, 48, 50, 53, 54, 77, 79, 155, 163, 164, 167, 297, 298, 299, 300, 301, 315 Dickson, 108 Dilution-pyrometers, 268 Dufour, 260 Dulong and Petit, 177, 191, 192, 193 Electric heating, 163, 310 Electric-resistance pyrometer, 10, 101 as a standard, 110 conditions of use, 119 experimental arrangements, 110 formula? for, 102, 106 law of, 104 nomenclature, 106 recording, 273 results with, 112 sources of error, 114 changes in constants, 118 compensation, 114 heating of, 114 insulation, 114 lag, 114 Emissive powers, 172, 204, 206, 214 Energy distribution, laws of, 179 curves, 181 Euchene, 93 Expansion coefficients : of gases, 17, 68 Expansion coefficients: of glass, 54 of iron, 51 of platinum, 50 of porcelain, 53, 54, 76 of quartz, 55 Expansion-pyrometers, 253, 256 Joly meldometer, 257 high-range thermometers, 259 Eye estimation of temperatures, 245 Fcry, 244, 245 absorption-pyrometer, 226 thermoelectric telescope, 198, 201 Fixed points, 6, 8, 68, 69, 70, 74, 76, 89, 90, 112, 113, 156, 295, 303, 307, 308 Furnaces: Barus rotating, 75 electric resistance, 310 iridium, 311 Fusible cones, 11, 262 Fusing-point, pyrometry, 261 Gasparin, 188 Gas-scale, 4, 17 Gas-thermometers, 9, 13, 17, 22, 48 at constant pressure, 14, 42, 62 at constant volume, 13, 36, 56 compensated form, 42, 63 correction to normal scale, 32 for high temperatures, 47, 79 indirect processes, 82 industrial, SI of Barus, 75 of Becquerel, 69 of Berthelot, 86 of Deville and Troost, 69 of Holborn and Day, 77 of Holborn and Wien, 76 of Jacquerod and Perrot, 79 of Mallard and Le Chatelier, 74 of Pouillet, 66 of Viollc, 71 recording, 271 substance of bulb, 49 volumetric, 15 INDEX. 339 Gay-Lussac's Law, 12 Glass, as gas-thermometer bulb, 77 exp?n?ion, 54 Gold, point of fusion, 298 Griffiths, 7, 296, 315 elect rical- resist ance pyrome- ter, 102, 104, 105, 112 Gruneisen, 53, 54 Hadfield, 316 Harker, 24, 26, 31, 34, 45, 105, 110, 296 Heat-radiation pyrometer, 187 conditions of use, 198 of Fery, 198 Hempel, 186 Henning, 55 Heraeus, 54, 55, 152. 164, 168, 169, 170, 311 Haycock, 5, 113, 118, 297, 300, 301, 313 Holborn, 7, 8, 48, 50, 52, 53, 54, 55, 72, 76, 77, 79, 103, 108, 135, 141, 154, 155, 163, 164, 165, 167, 297, 29S, 299, 300, 301, 302, 315 Holborn and Kurlbaum pyrome- ter, 237 Holman, 132, 154, 163, 301, 313 Howe, 167 Hydrogen-thermometer, 18, 20, 21 International Bureau. 20, 22, 26, 36, 110 Iridium, freezing-point, 302 -ruthenium couple, 168 Iron, as gas-thermometer bulb, 5 in calorimeter-pyrometer, 92 total heat of, 93 Isochromatic curves, 181 Jacquerod, 79, 299, 300 Job, 269 Joly, 195, 257 Joule and Thomson's expt., 30 Kirchoff, 173, 175 law of, 204 Kurlbaum, 175, 178, 244, 315 Laboratories, standardizing, 309 Langky, 179, 197, 198, 277 Lauth and Vogt, 262 Lawrence, 163 Le Chatelier, 52, 64, 74, 76, 93, 97, 140, 199, 219, 22!0, 226, 229, 254, 314,315,316 optical pyrometer, 208 adjustment of, 212 graduation, 216, 221 measurements, 213, 216, 220 modifications of, 226 precision and errors, 221 the photometer, 208 recording - pyrometers, 278, 291, 293 thermoelectric pyrometer, 122, 134, 144, 153, 154, 167, 278 Lummer, 173, 178, 180, 184, 244, 313, 315 Mahlke, 260 Mallard, 64, 74 Mariolte's Law, 12 Mascart, 285 Meier, 82, 86 Meldometer, 195, 257 Mercury-thermometers, 16, 259 Mesurt xad Nouel, 247 Moissan, 55, 314, 315 Monochromatic glasses, 211 Mylius, 55 Naphthaline, boiling-point, 307 National Bureau of Standards, 309 National Physical Laboratory, 105, 309* Nernst, 302, 311, 314, 315 Neville, 7, 113, 118, 297, 300, 301, 313 Newton, 177, 191, 192, 193 Nichols, 243 Nickel, in calorimeter-pyrome- ter, 93 total heat of, 94 Nitrogen-thermometer, 18, 20, 21, 25 compared with platinum, 105 Normal thermometer, 22, 36 340 INDEX. Optical pyrometer, 10, 204 conditions of use, 242 of Crova, 249 of Fery, 226 of Holborn and Kurlbaum, 237 of Le Chatelier, 208 of Mesure and Nouel, 247 of Morse, 241 of Wanner, 226, 229 Osmond, 167 Palladium, specific heat of, 73 thermoelectric properties, 121, 122 Paschen, 178, 183, 313 Perrot, 79, 299, 300 Pionchon, 93 Planck, Law of, 183, 313 Platinum, as gas-thermometer bulb, 36, 49, 67, 78 as resistance-thermometer, 101 fusing-point of, 72, 302 in calorimeter-pyrometer, 92 specific heat of, 71, 92 thermoelectric properties, 121 total heat of, 92 Porcelain, as gas-thermometer bulb, 51, 77 expansion of, 53, 54, 76 Pouillet, 13, 16, 92, 135, 188, 191, 299, 300 gas-thermometer, 66 thermoelectric pyrometer, 120 Pringsheim, 178, 180, 184, 244 Pyrometers, standardization of, 295 types of, 9 Pyrrh6liometre, 188 Quartz, as gas-thermometer bulb, 77 expansion of, 55 "Radiation, laws of, 171, 177 and temperature, 171 application to pyrometry, 185, 187 measurement of, 207, 245 Radiation-pyrometer, 9, 187, 198 of Fe*ry, 198 Radiomicrometer, 194 Rankine, 17 Rasch, 172, 302 Recording-pyrometers, 271 electrical resistance, 273 gas, 271 thermoelectric, 277, 291 continuous, 282 discontinuous, 279 Regnault, 7, 13, 16, 17, 18, 63, 83, 84, 89, 92, 113, 296 Reichsanstalt, 7, 50, 77, 105, 133, 141,309,313,315 Richards, 301 Roberts-Austen, 150,163,167, 285, 287, 288, 289, 290, 291, 316 recording-pyrometers, 282 Rose-Innes, 34 Rosetti, 177, 191, 194, 196 Roux, 283 Rubens, 183 Sainte-Claire-Deville, 16, 50, 51, 69, 71,82,83,84, 298 gas-pyrometer, 69 Saladin, 291, 293 Salts, fusing-points of, 307 Scheel, 55 Secchi, 191 Seger, 262, 316 Selenium, action of light on, 252 Shenstone, 55 Siebert and Kuhn, 54, 260 Siemens, 316 calorimeter, 97 electrical pyrometer, 101 Silver, fusing-point of, 300 Standardization of pyrometers, 295, 308 fixed points, 295, 308 laboratories for, 309 Standards, Bureau of, 309 Stansfield, 155, 163, 297, 301 Stefan, Law of, 177, 186, 188, 196 197, 198, 199, 201, 203, 315 Stewart, 244 Sulphur, boiling-point, 296 Tail, 121, 153 Temperature (see also Fixed points) INDEX. 341 Temperature and radiation, 171 definition of, 2 normal scale of, 12, 22 of a "black body," 176 of flames, 243 of industrial processes, etc., 167, 220, 221 of sun, 189, 191, 194, 220 Thermodynamic scale, 12, 26 and gas-scale, 26 calculation of corrections, 33 Thermoelectric pyrometer, 10, 76, 120 arrangement of wires, 146 chemical changes, 126 choice of couple, 124 cold junction, 151 conditions of use, 163 effect of heating, 166 electromotive force, 124 formulae, 121, 153 galvanometers for, 135 graduation, 152 heterogeneity of wires, 122 industrial applications, 167 industrial practice, require- ments of, 144 insulation and protection, 147 iridium-ruthenium, 168 junction of wires, 146 methods of measurement, 126 parasite currents, 126 principle of, 10, 76, 120 recent researches, 162 resistance of couples, 133 Thermometric scales, 3, 12, 26, 106 accuracy of, 9 normal scale, 22, 25 N and H scale differences, 21 Thermometric scales, platinum vs. gas, 105 Thermophones, 267 Transpiration-pyrometers, 268 Troost, 69, 82, 86 Tutton, 53 Tyndall, 177 Uhling and Steinbart, 270 ViUard, 55 Viotte, 6, 23, 72, 92, 190, 191 , 298, 299, 300, 302 gas-pyrometer, 71 Viscosity-pyrometer, 269 Volumetric thermometer, 15 corrections to, 64 Waidner and Burgess, 185, 221, 232, 236 Wanner pyrometer, 226, 229 description and calibration, 229 range and limitations, 235 sources of error, 232 Water, boiling-point, 307 Wedgwood, 1, 253, 254, 255, 316 pyrometer, 1, 253 Whipple, 112 Wiborgh, industrial air-pyrome- ter, 81 thermophones, 267 Wien, 8, 52, 72, 76, 103, 108, 135, 141, 154, 173, 299 laws of, 181, 182, 183, 184, 186, 198, 221, 231, 238, 300, 302, 313, 315 Wilson and Gray, 194, 196, 220 Zinc, boiling-point, 297 fusing-point, 297 SHORT-TITLE CATALOGUE OP THE PUBLICATIONS OF JOHN WILEY & SONS, NEW YORK. 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Railroad Engineer's Field Book. (In Preparation.) Searles's Field Engineering i6mo, mor. 3 oo Railroad Spiral i6mo, mor. i 50 Taylor's Prismoidal Formulae and Earthwork 8vo, i 50 *Trautwine's Field Practice of Laying Out Circular Curves for Railroads. i2mo. mor, 2 50 * Method of Calculating the Cubic Contents of Excavations and Embank- ments by the Aid of Diagrams 8vo, 2 oo Webb's Economics of Railroad Construction. . . .' Large i2mo, 2 50 Railroad Construction i6mo, mor. 5 oo Wellington's Economic Theory of the Location of Railways Small 8vo, 5 oo DRAWING. 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