Cornell University Library QC 277.L45 High-temperature measurements, 3 1924 004 250 423 Date Due m% \9tt' irtPl ELB i' ml rr-ter^ m^- r\M n lor 2- T^ - / ' OePARTM.;NT or HEAT-POWER ENGINCERING non Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004250423 Wedgwood Pyrometer. [FronlUiiiei-e .'\ HIGH-TEMPERATURE MEASUREMENTS. BY H. LE CHATELIER, Ingiiiieur en chef du Corps des Mines, Professeur de chimie minerale au College de France, 0. BOUD GUARD, Assistanty College de France. TRANSLATED BY GEORGE K. BURGESS, Instructor in Physics, University of Michigan, FIRST EDITION. FIRST THOUSAND. NEW YORK: JOHN WILEY & SONS. London: CHAPMAN & HALL, Limited. 190X. Copyright, 1901, BT GEORGE K. BtTHGESS. ROBERT DRtlMMOin), PRINTER, NEW YORK. AUTHOR'S PREFACE TO 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 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 iii iv AUTHOR'S PREFACE TO AMERICAN EDITION. 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 aUoys. Investigating the dilatation of the difEer- 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 iuto which silex and even quartz are transformed by suflBcient heating. In the same manner have been studied the dissociatioTi of the carbonate of Ume, 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 head 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 the question to attempt to give in this short preface the complete list. It wiU suflace to mention the most impor- tant among them, such as the following investigations : AUTHOR'S PREFACE TO AMERICAN EDITION. V The fusibility of metallic alloys has been the object of a very complete memoir by H. Gautier, and of important researches by Sir Eoberts Austin and by Heycock and Neville. 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, Ooupeau, Chautepi6. But the use of precise methods for the measurement of high temperatures is not limited to laboratory researches. It has 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. Parvill6 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, 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 vi AUTBOB'8 PREFACM TO AMERICAN EDITION. 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 Prance have the merit of having first utilized these new scientific methods. Euch^ne 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 Eoberts Austin 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 savants 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 Mr. 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 Chateliek. Pams, January 10, 1901. CONTENTS. PAQB Preface iu Introduction 1 Thermometric Scales 3 Fixed Points 5 Pyrometers 7 CHAPTER I. Normal Scale of Temperatures •. 10 Laws of Mariotte and Oay-Liissac 10 Gas-thermometers 11 Regnault's Experiments 14 Normal Scale of Temperatures 19 Thermodynamic Scale 21 CHAPTER II. Normal Thermometer 27 Sfivres Thermometer 27 Callendar's Thermometer 88 Thermometer f oi High Temperatures 86 CHAPTER III. 0AS-PTRO METER 37 Substance of the Bulb 37 Corrections and Causes of Error 40 Constant-volume Thermometer 40 Constant-pressure Thermometer 46 Volumenometric Thermometer 48 . vii viii CONTENTS. PAOE Experimental Besults SO Pouillet's Besearches 50 E. Becquerel's Besearches 53 Besearclies of Sainte-Clalre-Deville and Troost 53 VioUe's Besearches ^ , . . 55 Besearches of Mallard and Le Chatelier 67 Besearches of Barus 58 Besearches of Holborn and Wien 59 Arrangement of Experiments ... 60 Indirect Methods 62 Method of Crafts and Meier 63 Methods of H. Sainte-Claire-Deville 63 Method of D. Berthelot 66 Fixed Points 69 Sulphur 70 Zinc 70 Gold 71 SUver 71 Platinum 73 Metallic Salts 73 Table of Fixed Points 73 CHAPTEE IV. Calorimetric Pyeometbt 74 Principle 74 Choice of Metal 75 Platinum 75 Iron 75 Nickel , 76 Calorimeters 77 Precision of Measurements 80 Conditions of Use 82 CHAPTEB V. Electrical Bksibtance Pyrometer 83 Principle.... 83 Besearches of Siemens 83 Besearches of Callendar and Griffiths 84 CONTENTS. IX PAGE Researclies of Holborn and Wien 85 Law of Variation of Resistance of Platinum 86 Experimental Arrangement 88 Conditions of Use , 91 CHAPTER VI. Thekmoelectrio Ptrometer 93 Principle 93 Experiments of Becquerel, Pouillet, Regnault 93, 93 H. Le Chatelier's Investigations 94 Heterogeneity of Wires , 94 Choice of the Couple 96 Methods of Electric Measurements 99 Compensation Method 100 Galvanometric Method 101 Resistance of Couples 103 Galvanometers 103 Different Types of Galvanometer 107 Arrangement of the Wires of the Couple 113 Junction of the Wires 112 Insnlation and Protection of the Couple 113 Cold Junction 117 Graduation • 118 Formula 118 Fixed Points 119 Experimental Results • 136 CHAPTER VII. Heat-radiation Ptrometer 189 Principle 139 Pouillet'a Experiments 130 VioUe's Experiments 131 Rosetti's Experiments 133 Experiments of Wilson and Gray 135 Langley's Experiments 138 Conditions of Use 139 CONTENTS. CHAPTER VIII. PAGE Ltjminotis Eadiation Ptrometeb 140 Principle 140 KirchofE's Law 140 Measurement of the Total Intensity of Radiation 143 Measurement of the Intensity of a Simple Radiation 143 Le Chatelier's Pyrometer 144 Adjustment of the Apparatus 147 Measurements 148 Details of an Observation 149 Graduation , 153 Conditions of Use 155 Measurement of the Relative Intensity of Different Radia- tions 156 Use of the Unaided Eye 156 Use of Cobalt Glass 157 Telescope of Mesure and Nouel 158 Crova's Pyrometer 160 CHAPTER IX. Contraction Ptrometer (Wedgwood) 163 CHAPTER X. Fusible Cones (Seser) 167 CHAPTER XI. Recording Pyrometers 174 Recording Gas-pyrometer 174 Electrical-resistance Recording-pyrometer 176 Thermoelectric Recording-pyrometer 179 Discontinuous Recording 181 Continuous Recording 184 CHAPTER XII. Conclusion 193 CONTENTS. xi CHAPTER XIIL PAOB Recent Developments ^ 197 Qas-pyrometry I97 Thermoelectric Pyrometer 200 Platinum-resistance Pyrometer 204 Fixed Points 207 Radiation Pyrometers 207 Other Pyrometers 212 BrBLIOGRAPHICAL INDEX 216 HIGH TEMPERATURES. INTKODUCTION. 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 1783, in order to emphasize the importance of this question, Jie considers at length certain niatters 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 considerably depreciated by the excess or lack of very small quantities 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, Keplaced to-day by 2 RIQR TEMPERATURES. apparatus of a more scientific nature, it has been perhaps too readily forgotten. 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 attracted 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 temperature 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 thermo- metric body. But the second law is wanting; one cannot, by the juxtaposition of several bodies at the same tempera- ture, realize a system equivalent, from the point of view of exchanges of heat, to a body of different temperature INTBODVCTION. 3 thus temperature is not measured, at least insomuch as one considers only the phenomena of convection. In order to determine a temperature, one observes any phenomenon whatever varying with change of tem- perature. Thus for the mercury centigrade thermometer the temperature is defined by the apparent expansion of mercury from the point of fusion of ice measured by means of a unit equal to yj-j- of the dilatation between the tem- perature 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 measurement 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. Fahrenheit Reaumur Celsius Wedgwood Pouillet (Normal ther.) (Thermodyn. scale) Siemens Phenomenon. Dilatation j Permanent \ I contraction f Dilat. at const, p. Dilat. at const, v. J Reversible I I heat^cale } Electric resistance Substance. Mercury Origin. ( Very cold i winter Clay Dehyd rat Air Ice Hydrogen " Anything Heat = = Platinum Ice Unit. !■ 1/180 Ice to B. P. 1/80 " " " 1/100 " " " 1 /2400 init. dimeng. 1 1 1/100 Ice to boiling-point The enormous differences above mentioned in the measurements of high temperatures are much more the 4 BIOH TEMPERATURES. result of the diversity of the scales than due to the errors of the measurements themselves. Thus the experiments 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 35 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 thermometric 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 aU 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 ndt 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 aU measurements. One can take any thermom- eter, 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 wiU be advan- tage 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 princi- pally from its great dimensions and of its fragility. It is our purpose, in this introduction, to pass in review INTRODUCTION. 5 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 of this comparison which is still to-day the cause of the most important errors in the measurement of high temperatures. 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-thermom- eter; the actual precision of the measurements of high temperatures is entirely subordinate to that with which these fixed points are known; this precision is not very great because these fixed points have only been compared in an indirect manner with the gas-thermometer, and some of them only by aid of processes of extrapolation, always very uncertain. Violle was the first to make a series of experiments of considerable precision, which up to these 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 1300°. He made use indirectly of the relation thus established between specific heat and temperature to determine by comparison 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, . ( Ag Au Pd Pt F««OB ,,,...,,,.,,. I 951= jQ^g. jgoQo j7^go 6 man temper at ubbs. Finally, in a second series of experiments, he determined by direct comparison with the air-thermometer the boil- ing-point of zinc. ( Zn Boiling-point -j 029 g Barus, 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, T, .,. . . ( Cd Zn Uoiling-pomt -j ^^go j^^ J ij-g^o 926° and 931° Mean 778° 938°.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 : . ( Sn Bi Cd Pb Zn *'^^"'° 1233° 270° 832° 839° 421° Boiling-point ) Aniline Napthaline Benzopbenone Mercury Sulphur under 760 mm. f 184°.l 217°.8 305°.8 356°.7 444°.5 These last figures may be compared with Eegnault'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 following points of fusion : S° Z° (9^f« Sb AJ^j Ab Au Cu 233° 419° 633° 629°.5 654°.5 960°.5 1062° 1080°.5 Finally, Holborn and "Wien of the Physikalische Eeichsan- stalt of Berlin, have recently made a series of determina- tions, which seem, of all those made up to this time, to merit the greatest confidence. They have determined the INTRODUCTION. 7 points of fusion by means a thermocouple compared up to 1400° with the air-thermometer. )Ae Au Pd Pt 970° 1072° 1580° 1780° Mr. Daniel Berthelot, by quite recent experiments, has calibrated a thermocouple by comparison with the gas- thermometer, making use of the variation of the indices of refraction with the density. With this thermocouple he has determined the points of fusion : I Ag Au 962° 1064° From this collection of results we may conclude that the fixed points presenting actually the greatest reliability for the indirect standardization of the various thermo- metric scales are the following: Sn thSinl" ^° s ^'' ^' 2° ^e •*•" ^' Fusion.... 232° — 420° — 630° 655° — 962° 1065° 1780° Ebullition. — 218° — 445° — — 930° — — — We may consider these temperatures as known with an uncertainty inferior to : 1° between 200° and 500° 5 " 500 " 800 10 " 800 "1100 50 above 1100 In spite of the concordance between the two determina- tions of the fusing-point of platinum, one must entertain certain doubts of the precision of the number obtained; it results in the two cases from extreme extrapolations whose concordance may be fortuitous. Pyrometers. — Among the many proposed pyrometric methods, we shall dwell upon the following, the only ones which up to the present have been seriously employed. Gas-pyrometer (Pouillet, Becquerel, Sainte-Claire-De- viUe).— Utilizes the measurement or change in pressure of 8 HIGH TEMPEBAIXTBES. a gaseous mass kept at constant volume. Its great volume and its fragility render it unsuitable for ordinary measure- ments; it serves only to give the definition of temperature and should only be used to standardize other pyrometers. Calorimetric Pyrometer (Kegnault, Violle, Le Chatelier). — Utilizes the total heat of metals (platinum in the labo- ratory and nickel in industrial works). Is to be recom- mended for intermittent researches in industrial estab- lishments because its employmeat demands almost no apprenticeship and because the cost of installation is not great. Radiation Pyrometer (Kosetti, Langley, Boys). — ^Utilizes the total heat radiated by warm bodies. Its indications are influenced by the variable emissive power of the differ- ent substances. Convenient for the evaluation of very high temperatures which no thermometric substance can with- stand (electric arc, sun). Optical Pyrometer (Becquerel, Le Chatelier). — Utilizes the photometric measurement of radiation of a given wave- length of a portion of the visible spectrum. Its indica- tions, as in the preceding case, are influenced by variations in emissive power. The intervention of the eye aids greatly the observations, but diminishes notably their precision. This method is mainly employed in industrial works for the determination of the temperatures of bodies difficult of access — for example, of bodies in movement (the cast- ing of a metal, the hot metal passing to the rolling-mill). Electric-resistance Pyrometer (Siemens, Oallendar.) — 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 wiU merit the preference for very precise investigations in laboratories when we have a satisfactory determination of the variation INTBODUOTION. 9 of resistance of platinum in terms of the normal gas- thermometer. Thermoelectric Pyrometer (Becquerel, Barus, Le Chate- lier). — Utilizes the measure of electromotive forces dcTel- 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 galvanometer with movable coil, one has an apparatus easy to handle and of a precision amply suflficient considering the actual state of the means of standardization at our disposal in terms of the normal scale of temperature. This pyrometer is more generally used in scientific laboratories than in industrial works. 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 (Leger). — Utilizes the unequal fusibility of earthenware blocks of varied composition. Gives only discontinuous indications. Such blocks studied by Leger are spaced so as to have fusing-points distant about 20°. In general use in pottery works and in some similar indus- tries. CHAPTEE 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 Mariotte and Gay-Lussac are the basis for the use of the dilalation of gases for the determination of temperatures. These two laws may be written p,v, l+< ^' the temperatures being measured with the mercury- thermometer, a is a numerical coeflBcient, the same for all gases, at least to a first approximation, and its value is 0.00366 = ^y 10 BOBMAL SOALB OTP TEMPBRAtURE8. 11 ■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 d, 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 Eegnault. The expression for the laws of Mariotte and Gay-Lussac can be put in the form pv = nR(l + t) . . . . . (2) by calling n the number of units of quantity (this unit may be either the molecular weight or the gramme) ; B the value of the expression ^ + 'o 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. 12 HIGH TBMPERATUREB. The expression (2) then gives between the two tempera- tures t and t^ the relation from which t-h=P-pl^+t^ (3) 3. 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 1 = ^-+t n a ^'. from which t~t. 1+') (^) 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 (3) gives p _ n a- Po I'ri NORMAL SCALE OF TEMPERATURES. 13 from which t-t =P^o-P<,'n {^+to} ... (5) Pon 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 expres- sion (3) gives pv = «^(^ + t^, p'v = n'B[^+t), from which {p-p')v=in-n')R{^~+t), or i=_l+P^.^ (6) a n — n Ji This necessitates a preliminary determination of the con- stant E. In the particular case in which p' = 0, which supposes that a complete vacuum is obtained, the preceding relation becomes simpler and is ^ = -i + f I- W a n Ji 14 BIOS TBMPMEATtfMB. 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 PouiUet, Becquerel, Sainte-Olaire-Deville. Experiments of Regnault. — The very precise experiments of Eegnault 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 0° to 100° they do not present between these extreme temperatures very great differences, 0°.30 as a maximum, but at temperatures above 100° these differences may become considerable and reach 10°. Constant-vol. Air-thermom- eter, p„ = 760. Mercury-tbermometer in Crystal. White Glass. Green Glass. Bohemian Glass. 100° 150 300 250 300 350 + 0°.00 + 0.40 + 1.25 + 3.00 + 5.72 + 10 .50 + 0°.00 - 0.20 -0.30 + 0.05 + 1.08 + 4.00 + 0°.00 + 0.30 + 0.80 + 1 .85 + 3.50 + 0°.00 + 0.15 + 0.50 + 1.44 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 NORMAL 80 ALE OF TEMPEBATUMEB. 15 have them correspond with those which were observed with the difEerent 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 Kegnault 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 Mariotte is not rigorously exact; we have in reality pv = p^v, + 6, e being a very small quantity, but not zero. The experiments of Eegnault 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 0° and 100° : Volume Constant. Pressure Constant. 'ressure ). a 1 a Pressure. ^ 1 266 0.003656 273.6 760 0.003671 272.4 760 8655 273.8 2525 3694 270.7 1693 3689 371 2630 8696 270.4 3655 8709 269.5 For air at 4°. 5 Eankine obtains, from the experiments of Kegnault, the formula pv =p At 0° 100 200 300 500 1000 0.001173 0.000627 393 267 147 54 0.04 0.09 0.23 0.62 0.001173 0.000457 225 127 53 12 0.084 0.30 0.47 1.19 The deviations of the air-thermometer at high tempera- tures are thus very slight if concordance is established at 0° and 100°; we shall not have to occupy ourselves further with the difEerences between the indications of the thermodynamic thermometer and those of the gas-ther- mometer. It is possible to make use of these same experiments of Joule and Thomson to determine the absolute temperature of the fusion of ice on the thermodynamic scale. Here are the resvilts of the computation of Mr. Lehr- feldt; he gives the following corresponding readings of the gas-thermometer at constant volume and of the thermo- dynamic thermometer: Gas Ther. Thermodyn Ther. Hydrogen 273.08 372.8 Air 372.48 273.27 Nitrogen 273.13 273.3 Carbonic acid 268.47 \ fjt.-^l ^7A°°'^°°^ ( 373.48 (Natanson) The thermodynamic temperature of melting ice should be in all cases the same; the deviations come from the uncertainties in the measurements of the heat of expan- sion. We should, according to these results, adopt for the temperature of the fusion of ice + 273°.0 with an uncer- tainty in this number of at least 0° .2. CHAPTEE II. NORMAL THERMOMETER. Sfevres Thermometer. — This thermometer is a constant- volume thermometer filled with pure, dry hydrogen, under the pressure of 1 meter of mercury at the temperature of melting ice. It consists of two essential parts : the reser- voir, enclosing the invariable gaseous mass, and the manom- eter, serving to measure the pressure of this gaseous mass. The reservoir is made of a platinum-iridium tube whose volume is 1.03899 liters at the temperature of melting ice. Its length is 1.10 m., and its outer diameter 0.036 m. It is attached to the manometer by a capillary tube of platinum of 0.7 mm. diameter. This is as small as is safe to make this tube on account of the otherwise too slow establishment of pressure equilibrium. 27 28 mOE TBMPBBATURE3. This reseryoir is supported horizontally in a double box with interior water circulation. For the determination of the 100° mark indispensable for standardization, the reser- voir can be placed in the same way in a horizontal heater supplied with steam and composed of several concentric coverings. Manometer. — The manometric apparatus is mounted upon an iron support of 3.10- m. height, which is made of a railway rail firmly bolted to a tripod of wrought iron. The lateral parts attached to this rail, planed their entire length, carry sliding pieces to which are fastened the manometer tubes and a barometer. Pig. 3 represents, in a slightly modified form, the manometric apparatus. It is composed essentially of a manometer open to the air whose open arm serves as cistern for a barometer. The other arm, closed half-way up by a piece of steel, is attached to the thermometric reservoir by the capillary tube of plati- num. The two manometer tubes, each of 25 mm. interior diameter, have their lower ends fixed into a block of steel. They communicate with each other by holes of 5 mm. diameter bored in the block. A stop-cock permits closing this connection. A second three-way cock is screwed on the same block. One of its branches can serve to let mercury run out; the other, to which is attached a long fiexible steel tube, puts the manometer in communication with a large reservoir of mercury which can be raised or lowered the length of the support, either rapidly by hand, or slow-motioned by means of a screw. The barometer which sets in the open branch is fixed at its upper part on a carriage whose vertical displacement is regulated throughout a length of 0.70 m. by a strong screw. The latter is held at its two ends by two nuts which permit it to turn without longitudinal motion; it works in a screw attached to the carriage, and carries at its IfORMAL TMERMOMETES. 29 lower end a toothed pinion which works into a cog-wheel. It suffices to turn this wheel by acting upon the rod which serves as axis in order to raise or lower the carriage with EiG. 3. the barometer tube. This last has a diameter of 25 mm. in its upper part. The chamber is furnished with two indices of black glass soldered to the interior of the tube at 0.08 m. and 0.16 m. from the end. The points of these 30 Eias TEMPERATURES. indices, convex downwards, sensibly coincide with the axis of the barometric chamber. The part of the barometer which fits into the open manometer arm has a diameter greater than 0.01 m., and ends below in a narrower tube curved upwards. The piece of steel which ends the closed arm is adjusted to this tube like a cock, leaving between itself and the tube but a very slight space, which is filled with sealing-wax. It rests upon the upper rim of this tube, to which it is besides pressed by leather washers tightly screwed up. At its lower end it terminates in a perfectly smooth polished plane, which is adjusted to be horizontal. In the middle of this surface, near to the opening of the canal which prolongs the joining tube, there is fixed a very fine platinum point, whose extremity, meant to be used as a reference-mark, is at a distance of about 0.6 mm. from the plane surface. Above this piece is a tube of 25 mm. interior diameter, open above and connected below to the open arm of the manometer. Since the measurement of a column of mercury is more easily made and with greater precision when the menisci whose difEerence of level it is desired to find are situated along the same vertical, the barometer is bent so as to bring into the same vertical line the axis of the closed arm of the manometer and that of the barometer. Under these conditions, the communication between the two manometer arms being established, the total pressure of the gas en- closed in the reservoir of the thermometer is given by the difEerence of level of the mercury in these superposed tubes. The measurement of the pressures is made by means of a cathetometer furnished with three telescopes, each of which is provided with a micrometer and level. The micrometer circle is divided into 100 parts; at the distance NORMAL THERMOMETER. 31 from which the manometer is read, each division of the circle corresponds to about 0.002 mm. The method adopted for the measurement of pressures consists in determining the position of each mercury meniscus in terms of a fixed scale, hung near the manom- eter tubes, at the same distance as these latter from the telescopes of the cathetometer. One of the principal diflftculties arising in the measure- ment of pressures is that of the lighting of the menisci. The method employed by Chappuis consists in bringing up to the surface of the mercury an opaque point imtil its image reflected by the mercury appears in the observing telescope at a very small distance from that of the point itself. These two images being almost in contact, it is easy to set the micrometer cross-wire midway between them, at the precise point where would be the image of the reflecting surface. In order to have a very sharp image of the point, it is well to illuminate from behind by means of a beam of light passing through a vertical slit. The point and its image then stand out black on a bright back- ground. The use of styles of black glass is preferable to that of steel points on account of their unchangeableness and of the greater sharpness of their edges. The method with styles cannot be advantageously em- ployed except in wide tubes, where the reflecting surface of the mercury which aids in the formation of the image does not have a sensible curvature. Waste Space. — This consists of the space occupied by the gas : (1) in that part of the capillary tube which does not undergo the same variations of temperature as the thermometric reservoir; (2) in the piece of steel forming the plug which caps the closed arm of the manometer; (3) in the manometer tube between the mercury and the horizontal plane in which ends the piece of steel. The 32 HIGH TEMPERATURES. mercury is supposed to just toucl; the style serving as reference-mark. The capacity of the tube has been determined by mer- cury calibration; it was found equal to 0.567 cc. The length of the capillary tube being 1 m., if we deduct from this capacity that of 3 centimeters of the tube which are exposed to the same temperatures as the reservoir, that is 0.015 cc, this leaves 0.552 cc. The capillary tube fits for a length of 27 mm. into the piece of steel serving as plug. The total thickuess of this plug is 28.3 mm.; thus the portion of the canal included between the end of the capillary tube and the lower face of the plug is 1.3 mm. in length. As its diameter is 1.35 mm., the capacity of this canal is 0.0019 cc. The space included between a cross-section of the manometer tube passing through the style and the plane surface of the plug is 0.3126 cc. To have the total volume occupied by the gas it is necessary to add as well to this space the volume of the depressed mercury in the manometric tube caused by the curvature of the meniscus. The radius of this tube being equal to 12.235 mm., we find for this volume 0.205 cc. We thus have as the total of the waste space the sum of the following volumes : ce. Capacity of capillary tube 0.5520 Volume of canal in the plug 19 Capacity of the manometer tube between the style and the plane 3126 Volume of depressed mercury 2050 Total waste space 1.0715 When the mercury does not just touch the style, we shall have to add to this value, 0.4772 cc. per millimeter separa- tion of the style from the top of the meniscus. NORMAL THERMOMETER. 33 The expansion of the mefal of the bulb has been measured by Fizeau's method; this volume has at different tempera- tures the following values : Liters. 20° 1.03846 1.03899 30 1.03926 40 1.04007 60 1.04061 80 1.04117 100 1.04173 The variation of the capacity of the bulb due to changes of pressure has also been studied; per millimeter of mer- cury it is 0.02337 mm.'; or 3 For mm mm. " 100 3.3 " 300 4.7 " 300 7.0 " 400 :. 9.3 The zero is verified from time to time by bringing the bulb to the temperature of melting ice; there is absolute constancy even after heating to 100°. The deviation is at the most 0.03 mm. for a pressure of 995 mm. H. L. Callendar's Thermometer. — For the graduation of the platinum resistance-thermometer Callendar has studied an arrangement of the gas-thermometer in which the waste space is reduced to a minimum by an ingenious device which consists in interposing in the capillary tube a column of sulphuric acid which is always brought to the same position. It is then permissible to leave vacant spaces in the manometer of any volume, and this simplifies the measurements. The bulb is of glass, and its capacity is 77.01 cc. The capillary tube has a diameter of 0.3 mm. It is attached to a small U tube of 2 mm. diameter which contains the 34 HIGH TEMPERATURES. sulphuric acid. Tlie total value of the waste space is thus reduced to 0.84 cc. The sulphuric acid before each measurement is brought up to a reference-mark. The density of this liquid being one-seventh that of mercury, the errors made in determin- J fi^TrujTn^lre ^(PU}metr& Fig. 3. ing its level should be divided by seven to express them in heights of mercury. The use of this column of sulphuric acid has the inconvenience to oblige the experimenter to watch constantly the apparatus during the whole time of heating and cooling in order to maintain the pressure equilibrium in the two parts of this column; otherwise the liquid would be driven into the manometer or absorbed into the bulb. The manometer is one open to the air and is read con- jointly with the height of the barometer. NORMAL THERMOMETER. 35 The coefficient of expansion of the hard glass used in the construction of the thermometer was measured for a tube of same make by means of two microscopes carried upon a micrometer-screw. A cold comparison-tube could be placed under the microscopes to verify the invariability of their distance apart. MEAN COEFFICIENT OF EXPANSION. t a 17° 0.00000685 103 706 322 740 330 769 481 810 After heating to 400° there were permanent changes amounting to from 0.02 to 0.05 per 100. If the zero is taken at intervals of time of varying length, permanent displacements are noted. The following table gives some examples: Date. Oxygen- thermometer. Nitrogen- thermometer. Remarks. Jan. 21, 1886 " 22. '■ " 23, " " 25, " " 25, " mm. 693.1 692.9 692.9 693.0 693.0 mm. 695.4 695.1 694.9 693.8 694.1 j Filled at 300°; measure- 1 ment taken 4 days later After heating to 100° This change of zero has been attributed to a partial absorption of the air by the glass. Glass, an amorphous body resembling liquids somewhat, dissolves gases, espe- cially at high temperatures. For temperatures higher than 300° this source of error becomes very serious, especially if the gas is hydrogen. This gas disappears progressively by solution in the glass or by oxidation replacing elements of the glass. It is 36 EIGH TEMPERATURES. necessary to revert to nitrogen. This fact was observed by Chappuis and Harker in the course of a study of the platinum resistance-pyrometer when the temperatures measured reached as high as 600°. Thermometer for High Temperatures. — Up to the present time there has not yet been realized for the meas- urement of high temperatures a gas-thermometer suffi- ciently precise to be considered a normal apparatus. We shall point out, in studying the gas-pyrometers, the condi- tions that such an apparatus should fulfil, and the reasons for these conditions. We shall in this place give only a brief summary. The gas should be nitrogen. The bulb should be of porcelain enamelled inside and out. The measurements should be made by the method of the thermo-volumenometer or by any other method which does not entail an invariability of the gaseous mass throughout a very considerable period of time. In its actual condition the normal Sevres thermometer permits of measurements up to 100°. That of Oallendar has been employed up to 600°, and could without doubt with a porcelain bulb be used up to 1000°. It would be possible to reach, by the method of the volumenometer, 1300°. To go higher it would be neces- sary to manufacture a special porcelain less fusible than the ordinary hard porcelain, or, this failing, return to platinum in an oxidizing atmosphere, by which means it might be possible to reach 1600°. CHAPTER III. GAS-PYROMETER. The gas-thermometer, as we have seen above, need not of necessity be used for the measurement of temperatures ; it suflBices to make use of it for the standardization of the different processes employed in the determination of tem- peratures, but a priori there are not on the other hand any absolute reasons for discarding it in cases other than these standardizations. Indeed it has often been employed. We shall examine the various trials that have been made with it, and discuss the results of them. Substance of the Bulb. — The most important point to consider is the choice of the substance which constitutes the bulb; it is necessary to know its expansion to account for the variation of its volume under the action of heat; one must be sure of its impermeability. Three substances have been used up to the present time to make these bulbs : platinum, iron, and porcelain. Platinum, in spite of its high price, was employed by Pouillet and Becquerel; it has the advantage over iron in not being oxidizable, over porcelain in not being fragile. Its coefficient of expansion increases in a regular manner with the temperature : Between 0° and 100°. Between 0° and 1000°. Mean linear coefficient 0.000007 0.000009 In the course of a lively discussion between H. Sainte- Claire-Deville and E. Becquerel the former of those savants discovered that platinum was very permeable to hydrogen, a gas whose presence is frequent in flames at points where 87 38 HIGH TEMPERATURES. the combustion is not complete. Platinum was accord- ingly completely abandoned, perhaps wrongly; it is possible, in very many cases, to be sure of the absence of hydrogen, and the very precise experiments of Eandall have shown that red-hot platinum was quite impermeable to all gases other than hydrogen, even with a vacuum inside the apparatus. The only advantage of iron is its cheapness; it is as permeable to hydrogen as is platinum; it is not merely oxidizable in the air, but is besides attackable by carbonic acid and water-vapor. Thus the only gas that can be used with iron is pure nitrogen. The coefficient of expansion of iron is greater and increases more rapidly than that of platinum : Between 0° and lOO". Between 0° and 100°. Mean linear coefficient 0.000012 0.000015 Also this increase is not regular; there is produced at 850°, at the instant of the allotropic transformation, a sudden change of length, a contraction of 0.25 per cent. It is very difficult to obtain pure iron; very small quan- tities of carbon modify somewhat the value of the coefficient of expansion. Besides, the change of state of steel at 710°, corresponding to recaleseence, is accompanied in the heat- ing by a linear contraction, varying with the amount of carbon present, from 0.05 to 0.15 per cent. Porcelain was adopted as a result of the discussion between H. Sainte-CIaire-Deville and Beoquerel; it was considered as absolutely impermeable, but without decisive tests. Even well-baked porcelain consists of a paste somewhat porous and permeable; it is only the glazing that assures its impermeability. But this covering may sometimes not be whole; as it softens above 1000°, it is susceptible of cracking if left for a considerable time with an excess of pressure on the interior of the apparatus. According to GA8-P7R0METBS. 39 Holborn and Wien, the glazing is broken after reaching 1100°, when a considerable difference of pressure is estab- lished in the direction of the lifting up of this glazing. Finally like all verres, porcelain dissolves gases, and in particular water-vapor, which passes through it quite readily. A pyrometer left a long time in the flame at about 1300°, becomes filled with water-vapor which can be seen to condense in the manometer after a few weeks. The experiments of Crafts have shown that the rapidity of the passage of water -vapor through porcelain, in a pyrometer of from 60 to 70 cc. capacity at the temperature of 1350°, was 0.002 grm. of water-vapor per hour. It is thus not safe to employ porcelain at temperatures higher than 1000°, at least not in the thermometric processes which suppose the invariability of the gaseous mass. The expansion of porcelain has been the object of a great number of measurements which, for porcelains of very different make, give values near to one another; the mean linear coefl&cient between 0° and 1000° varies between 0.0000045 and 0.000005 for hard porcelain — that is to say, baked for a long time at a temperature in the neighbor- hood of 1400°. Here are the results of experiments made by Le Chatelier and by Coupeaux; the experiments were made with porce- lain rods 100 mm. in length, and the numbers below express the elongation of these rods in millimeters : Temperatures. 0° SCO" 400° 600° 800° 1000° 0.075 .078 .076 .090 0.166 .170 .168 .188 0.266 .270 .268 .290 0.367 .378 .360 .390 0.466 S&vres dure (cuite 3, 1400°). . . .470 Limoe'es .465 SSvres nouvelle (cuite a 1400°) .... .490 40 HIGH TEMPERATUBES. These numbers should be multiplied by three to give the cubical expansion. Porcelain has still another inconvenience: the glazing is put on the outside only of vessels, so that the porosity of the paste gives an uncertainty due to the unequal absorp- tion of gases at increasing temperatures. According to Barus, it is impossible to fill with dry air a pyrometer, not glazed inside, at ordinary temperatures. The water is not driven out by pumping out several times and letting in dry air. An apparatus filled in this way wiU indicate between melting ice and boiling water from 150° to 300°. Nor is filling the apparatus at 100° satis- factory: it wiU indicate 115° for this same interval of 100°. Barns thinks that at 400°, by repeating the operation sev- eral times, one can consider the apparatus as fiUed with dry air. 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 : P„F, = n,RT„ (1) P...V... = n,..RT.>., .... (2) PV = nBT. (3) Putting the first two series serve to determine — . a . It is preferable, except in researches of very great pre- GAS-PrBOMETEB. 41 cision, 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 , where H and H^ are the heights of mercury, J and A^ the densities of this metal. For a first approximation let us neglect the difEerences between Fand F„, n and w,,, A and <4„. We shall have then an approximate value T' for the temperature sought : ^'=M' (^) for a Let us find now the correction dT to T' to obtain the exact temperature. . In order to find this, take the logarithmic difEerential of (4) : T' - A„+ r„ n,- ■ ■ ■ ^> Then determine the values of the diilerent terms; let t^ and t, be the absolute temperatures of the surroundings when the bulb is at the temperatures 7" and T^. dA _ A-A^ ^- J. - ^. ' J = J„ . [1 - k{t, - Ql Tc = 0.00018(i;, - t,), 42 MIQB TEMPERATUBBa. ~=- 0.00018(^, - ^J. g dV V- V. °V= r,[l + k'{T'-T,)], A'(porcelaiii) = 0.0000135, ■^ = 0.0000135(7" - T.), by neglecting the variations of volume of the bulb due to changes of pressure. dn _ x^ — x^ in calling x^ and sTj the number of molecules contained in the waste space e at the temperatures t^ and t^. We have in fact, N being the total mass contained in the apparatus. n = N-x^, «. = N — x^. w — w„ = - {x,- x^). To determine a;, and x^ : P,^ i = x^Et,, Pi I = x^Rt, , dn __ ^(P P.] T, In noting that p r P. ~ n. we have dn _ _ elT' T,\ GAS-PTBOMMTES. 43 Put i-L±J2 =.*'-'- 2 After substitution we have dn _ e_^ (T' — T^ 6 T -\- T\ = -tA n, V, \ t t t r These successive transformations are for the purpose of making evident from the formula : 1. The ratio between the waste space and the total volume : — : 3. The temperature measured: T' — T^; 3. The variation of the surrounding temperature 8; which are the three essential factors on which depends the correction in question. Formula (6) then becomes: dT -f-i-- 0-00018(!(, - t^ + 0.0000135(!7" - T^ e T' - r„ y. \ t t T' - T \ Let us take a numerical example in order to show the importance of these correction terms in the three following cases : T' - T,= 500°, T' - T^ = 1000°, T' - T^ = 1500°. 44 HIGH TEMPEBATURE8. In taking f = 0.01, ^ = 27° + 373° = 300°, 26 z= 10°, we have dT^^, = - 1°.4 + 5°.15 + 13°.l = 16°.85, (?r„„. = - 2°.3 + 17°.0 + 38°.a = 52°.9, ^T,,„, = - 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 know. This 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 continuous 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 supposing that a complete and sudden change of temperature 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. QA8-PTR0METER. 46 To calculate this error, as in the ease of the corrections, "vre may employ the method of logarithmic differentials. Applying the same formula as before, we find for the relative error f: dT _ dV I T'-T, e T' + T\ T~ V,\ t t ' t )' and neglecting the second term of the parenthesis, which is relatively very small, dT^ _ _ dVi T' - T\ T - F. V t r Letting the section of the capillary tube be equal to 1 sq. mm., the volume of the bulb 100 cc, and assuming 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 : dT.,^. = 8°.5. 1»00 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 fr6m the changes of mass following the ingoings and outgoings of gas. As before, we have dT _ _ dn^ T ~ «/ Consider the experiments of Crafts. There enters per hour at 1350° in a bulb of porcelain of 100 cc, 0.002 grm. of water-vapor, or 0.225 milligramme-molecules; the 46 HIOH TEMPSRATVRES. initial volume enclosed at the start is 4.5 milligramme- molecules : '^^ «-^^^ = 0.05, T 4.5 which leads to an error of ^r„„» = 70° (about) for an experiment lasting one hour. This computation demonstrates clearly the enormous errors which may result from the penetration of an outside 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. 3. Constant-pressure Thermometer. — We still employ the same formula (4) : H/iV _ nRT H,A,V-n,RX which gives for a first approximation T^^n, T, n Calling t^ and t.^ the surrounding absolute temperatures corresponding to T^ and T ^ , «j and u^ the corresponding volumes of the waste space and of the reservoir, we have, for the determination of n and n^, the relations : «• = --- = f^. n — N—x^ = n^ — (x, — «,), HAu„ Rt, ' Rt. 0A8-PTR0MSTER. 47 As before, there is a correction to be applied to the approximate temperature T' thus obtained : dT dH dA dV H^ + A+r- T' ~ an expression the values of whose terms are known. 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 dT_dn^_dn _ d^f-. _ _^\ ^ dnJ T'- T\ T' ~ n, n ~ n,\ TJ~ n,\ T, J' As before, let Then we find dn 1 w. ~ " 1000 ■ dT,,. = r.5, dT,,., = 5°.0, dT^„^ = 9°.3. Thus the errors due to this cause are still greater than by the method of constant volume. In order to make exactly the correction for the waste space, the method of Regnault's compensator may be em- ployed, as in the work of Sainte-Claire-Deville and Troost; this allows of placing the measuring apparatus at a con- siderable distance from the fire, which makes the experi- ments much easier. Let us now examine the error resulting from the entrance of exterior gases : dT _ dn^__ dn^ ^ r ~ n ~ n' T: 48 BIGM TMMPEEATUBB8. For the experiment of Crafts, the error would be 413° instead of 70°, the bulb being filled at the start at atmos- pheric pressure. It is thus evident that, from all points of yiew, the method of constant volume is more precise than that of constant pressure; the lack of impermeability of the cover- ings is the only hindrance preventing the use of the former in practice. 3. Volumenometric Thermometer. — The only rational method for the measurement of high temperatures is, as we have already said, that of the volumenometer of Becquerel, which does not require the invariability of the gaseous mass throughout the duration of the experiment. It con- sists in measuring the changes of pressure resulting from a given variation of the gaseous mass contained in the bulb. Becquerel employed very slight changes of mass; the changes of pressure are then equally slight, which diminishes the precision of the measurements. There is no theoretical inconvenience in reaching an absolute vacuum, or, what is practically more simple, using the exhaustion given by a water-pump, as was done by Mallard and Le Chatelier; this considerably increases the precision. If the exhaustion is complete, we have the relation RT' ~ rt; M„ being the volume of the reservoir corresponding to the surrounding temperature T^. If the two volumes are filled under atmospheric pressure, P = P^, and then There are two corrections to make : the first relative to the expansion of the envelope, the second to the difference GAB-PYBOMETER. 49 between P and P^ when the exhaustion is produced by a water-pump : dT_^dP_ dV_ In general dP is in the neighborhood of 15 mm. of mercury, which gives dP p = 0.02. Also, ^ = 0.0000135(7" - rj, dT -^ = - 0.02 + 0.0000135(7" - T,). Calculating this correction for different temperatures, we have dT^,, = - 10°. 4, dT,,,, = - 8. 5, dT,,,, = - 0.35. 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 J" - Y ■ As before, assuming the higher limit to be xTnnr> dT _ 1 T' 1000' which leads to dT,„ = 0°.77, dT„„ = 1.27, dT^^, = 2.77. 50 SiaH 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 determination of the temperature of the pyrometer em- ployed. 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 pyrometer. 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 im- portant in the measurement of temperatures, especially of high temperatures, at which radiation becomes an impor- tant consideration. Within an enclosure whose tempera- ture is not uniform, which is true for the majority of furnaces, there may exist enormous differences of tempera- tures between neighboring parts. One cannot too strongly insist upon the presence of this source of error, with whose existence too many investigators have not sufficiently oc- cupied themselves. Experimental Results. — We shall study now the experi- ments made by various savants, and we sbaU 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 35 cm. in length; continu- ous with this tube was another of silver of the same QA8-PYR0METEB. 51 length, fastened to the manometer. The joining of the platinum and silver tubes was made by means of » metal Fig. 4. The ivaste space had thus a Yohime of Sf coUar (Fig. 4). 2 cc. The manometer was made up of tliree glass tubes em- bedded at their lower ends iu a metallic piece: the first tube serving as measurer was graduated in cubic centimeters, the second con- stituted the manometer properly speak- ing, and the third served to fill the apparatus. A cock convenient!}' placed per- mitted variation of the quantity of mercury contained in tlie apjiaratus (Fig. 5). The principle of this appa- ratus is the same as that of tlie more recent Eegnault 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 lip to 120°; there was comidete disaccordance with the readings of the mercury-thermom- eter; he attributes this non-agreement to the condensa- FiG. 5. 62 Hmn TEMPEBATUBEB. tion of air on the platinum. Becquerel showed later that this was due to the presence of water-vapor in the insuflB- ciently dried air. 2. Not being able to use the 100° mark for the determi- nation of the coeflBicient 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 VioUe : 100° 300° 500° 700° 1000° 1200° Pouillet, a =0.00375. ... '• a:= 0.00367 VioUe 0.0335 328 323 0.0843 336 535 0.0352 345 347 0.0360 353 359 0.0373 366 377 0.0380 373 389 Fusing-points. — Pouillet's determinations of fusing- points are far less good : Gold 1180° (too higli by 110°) 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 furnace 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 accu- rate measurements by this arrangement, certainly very irregular as to temperature, that the substance and the thermometer be in the same conditions with respect to radiation (Fig. 6). GAS-PTBOMETER. 63 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 fiisibility of alloys. Experiments of Ed. Becquerel. — 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. Boiling-point of zinc 930° (good) Pusing-point of silver 960 " Fasing-point of gold 1092 Fig. 6. Pyr. of Porcelain. 890° 916 1037 The iigures for gold differ among themselves by about 35°, more or less. It is diflftcult 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- Glair e-Deville and Troost. — They, after their discussion with Becquerel, made numer- 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 54 HIGH TEMPEBATUBE8. 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 fiUed 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 : Oas. First Series. Second Series. Third Series. Air From 945° to 955° " 925 to 924 1067 From 940° to 948° " 916 to 924 1079 From 928° to 933° Hydrogen . . . Carbonic acid . 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- ing of the cock placed at the outlet of the pyrometer. Troost found in this way 665° for the boiling-point of se- lenium; this figure is too high. As in the case of the de- termination of the boiling-point of zinc, the arrangement GAS-PTROMETEB. 55 for heating did not protect sufficiently against the radiation from the outer surfaces. Violle's Experiment. — Guided by H. Sainte-Olaire- Deville, whom his successive failures had instructed in the difficulties of the problem, VioUe 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 uncertainy 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 grms. 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 method of immersion; the numbers found vary from 0.0375 to 0.0379; mean, 0.0377. Near 1300° the measurements were made at constant pressure and at constant volume. 56 HIGH TEMPERATURES. Temperature at Constant Volume. Temperature at Constant Pressure. 1165° 1166 1192 Mean. Specific Heat of Platinum. 1171° 1169 1195 1168° 1168 1198 0.0388 .0388 .0389 The mean specific heat may be represented by the formula C,' = 0.0317 + 0.000006 . t. The true specific heat is equal to -^ = 0.0317 + 0.000013 . t. at VioUe 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. Eepeat- 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 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,' = 0.0583 + 0.000010 . t. GAa-PTROMETER. 67 The true specific heat is equal to 4t = 0.0583 + 0.000020 . t. at The fusing-point was found equal to 1500°; the more recent experiments of Holborn and Wien give 1580°. This diEEerence can be explained by impurities in the metal and absorption of furnaces-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 VioUe has deter- mined the boiling-point of zinc. He employed an ap- paratus of enamelled casting, heated in a triple enrelope of metallic vapor; the top was covered with clay and cow- hair to prevent su,perheating of the coverings. The measurements were made with pressure and volume simultaneously variable. Vplume of bulk. . . . 294.5 cc. Volume of gas let out 184.3 cc. Waste space 4.7 " Pressure 893.3 mm. T = 939°.6 U 3°.8 U r.i H„ 760.5 mm. Ho 759.5 mm. Barus, Holborn and Wien found numbers very close to 930°. 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 (" " "30) Experiments of Mallard and Le Chatelier. — In their investigations on the temperatures of ignition of gaseous mixtures. Mallard and Le Chatelier made i^e of a porcelain pjrrometer, which was exhausted; then air was let in and the gaseous volume thus absorbed was measured. It is possible 58 HIGH TEMPBRATURSa. to reach 1200° without noticing any breaking down of the porcelain; but this giving way is complete at 1300° under the action of the yacuum. 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 temperature 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 mixture with that of the air introduced under the same conditions of temperature, at least in the cases of mixtures burning with contraction. The pyrometer used had a capacity of 63 cc, after de- duction of the waste space (1 cc.) ; the following table gives the volumes of air corresponding to different temperatures : 400° 26.7 cc. 600 20.6 800 16.7 1000 14.1 1200 12.3 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 insuflScient volume of the thermometric reservoir. Experiments of Barus. — This American savant devised a rotating apparatus, remarkable for its uniformity of tem- perature, but he applied it directly only to the standardiza- tion 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 bismuth was found equal to 1200° under a reduced pressure of 150 mm., which would give under atmospheric pressure by extrapolation 1500°. OAS-PTMOMETMB. 59 Fig. 7 represents the longitudinal section of Barus' apparatus. It is composed essentially of a porcelain Fig. 7. pyrometer containing an interior tube in which is placed the couple. The pyrometer fixed at a point of its stem is held immobile. It is surrounded by a muffle of casting whose general shape is that of revolution about the axis 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-Eh proposed by Le Chatelier. They made use of a porcelain reservoir of about 100 cc. capacity, terminating at its two ends in capillary porcelain 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 60 EieH TEMPBRATURES. points the real temperature of the waste space whose Tolume 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 1300° 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 are to be counted among those which seem to merit the most 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. 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. The bulb of the thermometer should be of porcelain enamelled inside and out, as were the bulbs made at Sevres for certain experiments of Eegnault and of H. Sainte-Claire-Deville. The capacity of the bulb should be as nearly as may be GA8-PTR0MBTER. 61 as great as 500 cc, the condition necessary in order that the error resulting from the waste space be certainly less than 1°. The thermometric gas will be nitrogen. The volumenometer method will 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 porcelain 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. 62 HIGH TEMPERATUBE8. INDIRECT PROCESSES. We will place in this list yarious 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. 8) consists of a porcelain bulb, V 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, tmd consequently diminishes the pre- cision of the determinations. This method is especially con- venient 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 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. a \ v_y Fig. 8. GAS-PYROMETER. 63 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 pumice-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 : 3. 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-Glaire-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 ofE by the oxyhydrogen flame with the autog§ne solder. 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 = 73 cc. 64 HIGH TEMPERATTJRES. The computation may be made also in this way: Let 17° be the surrounding temperature; T^ = 273° + 17° = 290°. T' = 290 X 9r = 1150°. The correction due to the expansion of the porcelain is 0.0000135 X 850 = 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 diflBiculty 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. 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 *Thi3 result differs slightly from that given by Sainle-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. GA8-PTR0METES. 65 * 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 = 0.299 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 1.293 X 8.716 X 0.277 X ~ = 2.92 grm. The weight of iodine remaining in the reservoir is, taking note of the correction to be made resulting from the 2.16 grm. air which occupy 8.9 cc. at 930°, 27S 0.299 + 1.293(0.277 - 0.00216)^757^ = 0.634 grm. If there had been no air, the weight would have been 0.634 X ^;^ = 0.652 grm. T^ _ 2.920 ~T\ ~ 0.653' T' = 1290°. Making the correction for the expansion of porcelain (15°), we have T' = 1390 - 273 - 15 = 1003°. 66 BIQH TEMPERATURES. The difference between the result of this computation and that of DevHle comes from similar reasons to those noted above (page 64, note 1). 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 0.93 0.80 0.66 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 150°, which is far too low. Method of Daniel Berthelot.—Mi 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 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 OA8-P7R0METEB. 67 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 fringe 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 difEerence of phase Pig. 9. which renders the fringes invisible with white light. This is done in the following way (see Fig. 9) : A beam of light ab falls on a mirror MM', which breaks it up into two parallel beams, hf and cd; in order to separate the beams so as to be able to place apparatus conyeniently with respect to them, a prism P gives to the beam J/ the direction gh; one can thus secure a separation of 92 mm. A second prism P^ brings the beam cd into Im, and after reflection from a second mirror, M^M^, the 68 man temperatures. fringes are observed in a telescope focussed for parallel rays. The tubes containing the gases are placed at T and r,. It is evidently necessary that the prisms P and P, 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 diJBB.culty 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 wt.ter 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 re — 1 = led. In the constant-pressure tube ^ = Z < P.' To obtain the invariability of the fringes it is necessary that («. - n,)L = {n' - n„)l, GAS-PTBOMETER. 69 L being the length of the cold tube, and I the displace- ment of the warm tube ; k{d, - d,)L=^ kid' - d„)J, an expression which gives a relation between the pressures and the temperatures. This method, employed for the control of the boiling- points, has given the following results which are near those calculated from the old experiments of Regnault. Prpssiiro Temperature Temperature "*^'"*- Observed. Calculated. Alcohol 741.5 mm. 77°.69 77°.64 "Water 740.1 99 .2 99 .20 " 761.04 100.01 100.01 Aniline 746.48 183 .62 183 .54 " 760.91 1S4 .5 184.28 Berthelot has standardized by the same method a couple which he used to determine the fusing-points of silver, copper, gold, and the boUing-point of zinc : Silver 962° Gold 1064 Zinc 920 Cadmium 778 Except for the zinc, the numbers found are identical with those which result from the best determiaations made by other methods. The difference observed for the zinc is probably due to the radiation from the coverings of the vessel containing the metal. Fixed Points. — The fixed points which will be employed for the graduation of other pyrometers should be chosen from among the temperature-determinations made with the gas-thermometer. Among those that we have ex- 70 SIGH TEMPERATURES. amined, hardly others than the following are to be recom- mended : Sulphur. — (Boiling) 445° under a pressure of 760 mm., with a yariation of 0°.095 per millimeter change of mercury in the atmospheric pressure. The boiling-point of sulphur has been the object of four series of distinct determinations : Regnault 448' Crafts 445 Callendar 444 .5 Chappuis and Harker 445 .2 Regnault's figure was obtained by plunging the reservoir of the thermometer in the liquid sulphur; this liquid can superheat and gives too high a number. The other three very concordant observations were obtained in the vapor. They lead to the mean value of 445°, which should be accurate to at least 0°.5. Zinc. — (Boiling) 930°, with a variation of 0°.15 for a change of 1 mm. in the atmospheric pressure. The boiling-point of zinc, as that of sulphur, has been the object of numerous observations: E. Becquerel *. 930° and 890° H. Sainte-Claire-Deville 915 to 945 Barus 936 and 931 Violle 929.6 D. Berthelot 930 The values obtained by Violle and Barus which seem the most worthy of confidence lead to the adoption of the approximate value 930°, which should be exact to 5°. We have omitted in the above table the determinations of H. Sainte-Claire-Deville made with the vapor of iodine and the carbonic-acid thermometer, which give figures 100° higher and are certainly much too high. OAS-PTROMETER. 71 Gold. — (Fusion) 1065°. The determinations of the fusing-point of gold, also quite numerous, are still less con- cordant than those of the boiling-point of zinc. Pouillet 1180° K Becquerel 1092 and 1037' Violle 1045 Holburn and Wien 1070 to 1075 Heycock and Neville 1062 D. Berthelot 1064 The last four determinations a priori seem to merit an equal confidence. But the comparison between the fusing- point of gold by Violle, 1045°, and his fusing-point of silver, 954°, gives only a difference of 90°. On the other hand, by means of thermoelectric couples it is easy to establish •with certainty that the difference between these two tem- peratures is greater than 100°, although not much above this figure. Besides, the experiments of Violle on the fusing-point of silver are among the best. On this basis, we would find 1060° for the fusing-point of gold. By limiting ourselves to the last three series, we may take the approximate number 1065°, which should not have an error greater than 10°. Silver. — (Fusion) 962°. The fusing-point of this metal is of a less advantageous use than that of gold, by reason of its volatility, which does not allow of heating it near platinum wires (thermoelectric couple), as it alters them decidedly, and also by reason of greater changeability of fusing-point. In reducing atmospheres in contact with siliceous matters, the fusing-point is lowered markedly, on account probably of an absorption of silicium, as happens with platinum. The fusing-point of silver is one which has been the most often determined. 72 Hien TEMPERATURES. Pouillet 1000° E. Becquerel 960 and 916° Violle 954 Holborn and Wien 970 Heycock and Neville 960 .5 D. Berthelot 962 The last four determinations which seem to merit equal weight give a mean value of 963°, which should certainly be exact to at least 10°, very probably even to 5°. Platinum. — 1780°. The fusing-point of platinum has been determined twice by Violle in the first place, and then by Holborn and Wien. The results differed by only 1°, that is to say, they were practically identical. This accord, however, shoxild be only considered as a lucky chance, which can give no indication of the accuracy of the deter- mination of this fusing-point. The experimental measure- ments, and above all the indispensable extrapolations, involve greater uncertainties that cannot be known a priori. An error of 35° would not be incompatible with the precision of the measurements made. Sometimes it is desired to graduate a pyrometer down to the temperature of the surroundings, even if in this case the use of the mercury-thermometer is to be preferred. Use may then be made of the two boiling-points of water and naphthalin. Water. — 100°, with a variation of 0°.04 for a change of 1 mm. in the atmospheric pressure. Naphthalin. — 318°, with a variation of 0°.06 for a change of 1 mm. in the atmospheric pressure. Metallic Salts. — The different fixed points that have been mentioned are not all of a very convenient use. It would be, preferable to have, in place of the metals, metallic salts for the determination of the fixed points. These salts in fact are for the most part without action GA8-PTB0METES. 73 on platinum, which, is a great advantage for the standard- ization of thermoelectric couples. There are none, unfor- tunately, whose fusing-points have been determined up to the present time in a sufficiently precise manner. Among the most interesting to study, from this point of view, we may cite the following : 1 mol. NaCl + 1 mol. KCl About 650° NaCl NajO.SO,.... PbjO,.2NajO. MgO.SO SiOj.CaO 800 900 1000 1150 1700 Table of Fixed Points. — In the actual state of our knowledge the fixed points to which we should give prefer- ence are summarized in the table below : Ebullition. Fusion. Water 100° Naphthaline 218 Sulphur 445 Zinc '. 930 Silver '. 962° Gold 1065 Platinum 1780 CHAPTER IV. CALORIMETRIC PTEOMETET. Principle. — A mass ^ of a body, brouglit to a tempera- ture T, is dropped into a calorimeter containing water at a temperature t^. Let t^ be the final temperature of water and substance. P being the water-equivalent of the sub- stances in contact (water, calorimetric vessel, thermotaeter, etc.) which are raised from t„ to t^, XJ' the heat required to warm unit mass of the body from t^ to T, we have Lf xp = P{t, - Q. Taking as origin of temperatures the zero of the centi- grade thermometer, the heat required to warm unit mass of the body to the temperature T will be The quantity Z„, is easy to calculate, because the specific heats at low temperatures are suflBLciently well known : l: = ct,. The expression for the total heat becJcftiles' l; = ^2^) + .,,. ij and t, are the temperatures given by the direct readings of the thermometer. The value of the second member is thus wholly known, and consequently that of the first member which is equal 74 CALOBtMETBIO PtJROMaTRT. t5 to it. If previous experiments have made known the value of the total heat Zf for different temperatures, one may from the knowledge of if determine the value of T. It will be sufficient to trace a curve on a large scale whose abscissas are temperatures, and ordinates total heats, and to find upon this curve the point whose abscissa has the value given by the calorimetric experiment. Choice of Metal. — Three metals have been proposed: platinum, iron, and nickel. Platinum. — This metal was first proposed by Pouillet, and taken up again by VioUe. It is much to be pre- ferred to the other metals; its total heat has been com- pared directly with the indications of the air-thermometer. This metal can be probably reproduced identical with itself. Iridium, which commercial platinum often carries, has the same specific heat. The high price of these substances is an obstp,cle to their use extensively in works ; for a cal- orimeter of a liter it is necessary to have at least 100 grms. of platinum, — or $100 in a volume of 5 cc, — ^easily lost or made away with. VioUe determined the total heat of platinum from 0° to 1200°, and computed by extrapolation up to 1800°. 100° 3.23cal. 1000° 37.70 cal. 200 6.58 1100 42.13 300 9.75 1200 46.65 400 13.64 1300 51.35 500 17.35 1400 56.14 600 21.18 1500 61.05 700 25.13 1600 66.08 800 39.20 1700 71.23 900 33.39 1800 76.50 Iron. — Eegnault, in a study made for the Paris Gas Company, had proposed, and caused to be adopted, iron, in attributing to it a specific heat of 0.136, while it is, at 0°, 0,106. He used a cube of 7 cm. sides which was thrust 76 BIQH TEMPERATUBEa. into the furnaces by means of long iron bars. The calorimeter was of wood and had a capacity of 4 liters. Various observers have determined the total heat of iron; at high temperatures the accord is not perfect among the results. Temperature. Post. Pionchon. EuchSne. Mean Specific Heat. Degrees. Calories. Calories. Calories. Calories. 100 10.8 11.0 11.0 10.8 200 22.0 22.5 23.0 21.5 300 35.0 36.5 37.0 32.5 400 39.5 41.5 42.0 43.0 500 67.5 68.5 69.5 54.0 600 86.0 87.5 84.0 65.0 700 108.0 111.5 106.0 76.0 800 132.0 137.0 131.0 87.0 900 157.0 157.5 151.5 98.0 1000 187.5 179.0 173.0 109.0 But this metal is not at all suitable for such use, by reason in the first place of its great oxidability. There is formed at each heating a coating of oxide which breaks off upon immersion in water, so that the mass of the metal varies from one observation to the next. Besides, iron, especially when it contains carbon, possesses changes of state accompanied during the heating by a marked absorp- tion of heat. By cooling in water, tempering takes place which may irregularly prevent the inverse transformations. nickel. — At the Industrial Gas Congress in 1889 Le Chatelier proposed nickel, which is but slightly oxidizable up to 100°, and which above 400° does not possess changes of state as does iron. The total heat of nickel has been determined by Pionchon and by Euchdne and Biju-Duval. The differences are due very probably in part to impuri- ties that the nickel may contain. CALOlilMBTBIC PTSOMETHr. 77 Temperature. Konchon. Euchdne. Degrees. Calories. Calories. 100 11.0 12.0 200 23.5 24.0 300 42.0 37.0 400 52.0 50.0 500 65.5 63.5 600 78.5 75.0 700 92.5 90.0 800 107.0 103.0 900 123.0 117.5 1000 138.5 134.0 Calorimeters. — 1. In laboratories there is employed with the platinum mass Berthelot's calorimeter, a description of which is given in the Annales de Ohemie et de Physique* (Fig. 10). The thermometer used for the Fig. 10. measurement of the rise in temperature should be very sensitive, so that a rise of from 2° to 4° be sufiBcient in * 4th Series, t. xxix. p. 109 ; 5tli Series, t. v. p. 5 ; t. x. p. 433 and 447 ; t. xii. p. 550. 18 mOB TEMPBRATUBE8. order to render negligible the cooling correction. If use is made, for instance, of a thermometer giving the hundredth of a degree, the mass of platinum should be about one-twentieth the mass of the water in the calorim- eter. 2. In the arts, where the measurements are made with less precision, and where it is necessary to consider the cost of installation of the apparatus, nickel will be made use of, a thermometer giving tenths of a degree, and a zinc calorimeter, which may be home-made. Such an installa- tion may cost as little as $4. A mass of nickel should be used equal to one-twentieth of the mass of water of the calorimeter. The calorimeters used by the Paris Gas Company are after the Berthelot pattern. They are also water-jacketed calorimeters, of which there are two types. Water-jacketed Calorimeters. (Figs. 11 and 13). — These ^-^ ^51- E ^rf Fi&. 11. A, cylindrical vessel of thin copper ; B, water-jacket ; C, wooden support ; D, handles ; E, filling-tubes ; F, felt jacketing. apparatus consist of a cylindrical calorimeter of two liters capacity, of zinc or of copper; a double cylindrical jacket CALORIMBTRIC P7R0METBY. 79 of the same metal, containing water and surrounded bj' felt on the outside. The calorimeter rests on this jacket by means of a wooden support. A thermometer graduated to Aism ¥™ ^TO. J U J, E :B- E, filling-tube; Fig. 12. A, zinc vessel ; B, water-jacket ; C, cork supports ; &, cardboard cover. fifths of a degree, having a small but quite long bulb, serves as stirrer. The thermometric substance is a piece of nickel of mass equal to one-tenth that of the water, or 200 grms., so as to have considerable rise of temperature easy to read by the workmen who make the measurements. As a general rule, one must avoid placing the thermo- metric substance upon the floor of the furnace. The piece of nickel, which is made in the form of small cylinders having from 15 to 25 mm. diameter and from 10 to 30 mm. length, rests so as to be insulated from the floor in a nickel crucible provided with a foot and with two arms attached somewhat above the centre of gravity. When it has been heated for a half-hour an observer takes out the crucible with a forked rod, and another ^^- ^^■ seizes this crucible with tongs to empty it into the calori- meter. Use is not made of an iron crucible because this metal 80 MIOH TBMPBBATUtlBS. oxidizes and lets drop scales, which falling into the calorimeter would vitiate the experiment. Inside of a nickel crucible one can use pieces of fire-clay of the above form (Pig. 13). Precision of the Measurements. — Biju-Duval has made a series of experiments to study the sources of error arising from the use of the calorimeter by comparing its indica- tions to those of the thermoelectric pyrometer of Le Ohatelier. The observations were taken by varying the following conditions : Use of thermometer graduated to -|^° or to -^°. Use of the old wooden gas-works calorimeter or of the water-jacketed calorimeter. Use of iron or nickel. I. Experiment. — Old wooden gas-works calorimeter. Iron. Thermometer in fifths. P = 10000 grm. p = 1031 " t, = 20°. 8 t, = B6°.2 QJ = 153.5 cal. Computed temperature: Mean specific heat of iron = 0. 108 t = 1420° " " " = 0.126 t = 1210 Heat-toning according to Biju-Duval = 915 Thermoelectric pyrometer = 970 It is thus evident that the mean specific heats even with the correction suggested by Eegnault give tempera- tures much too high. With the curve of total heats the temperature found is much too low on account of the fol- lowing losses of heat : 1. Absorption of heat by the wooden walls; CALORIMMTRIC PTROMETRT. 81 2. Eadiation from the iron cube during transfer; 3. Cooling of the water in the calorimeter, whose tem- perature exceeded by 16° the temperature of the surround- ings. The following experiments were made with the ther- mometer reading to -^°; the piece of nickel was protected against radiation by a crucible. The two calorimeters were compared. II. Trial with the Wooden Calorimeter. T = 975° by the thermoelectric pyrometer P = 10000 grm. p = 145 " t„ = 20°.21 t, = 31°. 99 L/ = 125 cal. L/ = 130 cal. from the curve at 975° The difference is 5 calories, or 4 per cent loss due to the jacket. III. Trial with the Water-jacketed Calorimeter. T = 985° P = 2000 grm. jp = 48.4 " t, = 18°.86 t, = 21°.95 LJ = 130 cal. Lf =z 131.5 cal. from the curve at 985° The difEerence is 1.5 calories, or a loss of only 1.11 per cent when use is made of a carefully made calorimeter and of a thermometer giving -gij". This corresponds to an uncertainty of less than 10° in the temperatures sought. With the ^° thermometers, necessitating a much greater rise of temperature of the water in the calorimeter, an uncertainty of 25° wiU exist. 82 HIOH '1EMPERA2VBBS. Conditions of Use. — The advantages of the calorimetric pyrometer are : 1. Its low net cost; 2. The ease of its use, which allows of putting it in the hands of a workman. ' Its inconveniences are : 1. The time necessary to take an ohservation, ahout a half -hour; 3. The impossibility of taking continuous observations; 3. The impossibility of exceeding 1000° by the use of the piece of nickel. Its use does not seem to be recommendable for labora- tories. It is to be recommended for works in the cases where it is required to make only occasional measurements; in cases where there is not the personnel sufficiently skilful to use the more precise methods; and finally where the importance of the measurements is not such as to justify the buying of more costly instruments. CHAPTER V. ELECTRICAL RESISTANCE PYROMETER. Principle. — In this apparatus use is made of the varia- tions of electric resistance of a platinum wire as a function of the temperature; these variations are of the order of magnitude of those of the expansion of gases. The ratio of the resistances is 1.34 at 100°, and 4 at 1000°. As elec- tric resistances are measurable with great accuracy, this process of estimation of temperatures offers a very great sensibility, and it will be able to give very good results when we know exactly the law that connects the variations of resistances to those of temperature. The electric pyrometer was proposed by Siemens in 1871 (Bakerian Lecture) ; it rapidly came into use in metal- lurgical works on account of the reputation of its inventor, but it was soon abandoned for reasons which will be given later. Investigations of Siemens. — The Siemens pyrometer consists of a fine platinum wire 1 m. long and 0.1 mm. in diameter, wound on a cylinder of porcelain or fire-clay; the whole is enclosed in an iron tube, destined to protect the instrument from the action of the flames. Siemens tried also, but without success, ceramic matters impregnated with metals of the platinum group. To measure resistance he employed either a galvanom- eter, for laboratory experiments, or a voltameter, for the measurement in works. In this latter case the current from a cell divides between the heated resistance and a standard resistance at constant temperature; in each one 83 84 HIGH TEMPERATrilE8. of the circuits was placed a voltameter : the ratio of the volumes of gas set free gives the ratio of the current strengths and thus the inverse ratio of the resistances. Finally Siemens gave a formula of three terms connect- ing the electrical resistance of platinum to temperatures on the air-thermometer, but without publishing the ex- perimental data on which this graduation was based. Experiment soon showed that the apparatus did not rest comparable with itself. A committee of the British Association for the Advancement of Science found that the resistance of platinum increases after heating. It would be necessary then to graduate the apparatus each time that it was used. This change of resistance is due to a chemical alteration of platinum, which is enormous when directly heated in the flame, less, but still marked, if placed in an iron tube, and which disappears if use is made of a platinum or porcelain tube. This augmentation of resist- ance may reach 15 per cent by repeated heatings up to 900°. Platinum being very costly and porcelain very fragile, it was impossible to use these two bodies in the industries, which alone at that time occupied themselves with meas- urements of high temperatures, and this method was abandoned completely during twenty years. Investigations of Callendar and Griffiths. — These savants have revived this method for laboratory purposes; it seems the best for work of precision, on the condition of being assured of the invariability of the resistance of platinum. Callendar found that clay helps to cause the variation of resistance, that the platinum wire becomes brittle on its support and sticks there; this action is probably due to impurities in the clay. "With mica, on the other hand, which the wire touches only at the edges (the reel is made ELECTRICAL liEBISTANCE PYROMETER. 85 of two perpendicular slices of mica), there is perfect in- sulation without cause of alteration; but mica becomes dehydrated at 800" and then becomes very fragile. All metallic solderings should be proscribed, for they are volatile and attack platinum. Pressure joints (screw or torsion) are equally bad, for they become loose. One should use only the "autog^ne" solder by the fusion of platinum. Copper conductors should also be rejected, at least in the heated portions, on account of the volatility of the metal. A pyrometer with such conductors, heated during an hour at 850°, showed an increase of resistance of ^ per cent. Investigations of Holborn and Wien. — These savants have made a very complete study of this alterability of platinum wires, in a comparison between the methods of measurement of temperatures by electric resistance and thermoelectric forces; they work with wires of 0.1 mm. to 0.3 mm. diameter. They soon found that above 1300° platinum commences to undergo a feeble volatilization which suffices to augment notably the resistance of the very fine wires. Hydrogen in presence of silicious matters causes about 850° a rapid alteration of the platinum. Below are the results relative to wires of 0.3 mm. of a length of 160 mm. Wire a. R at 15°. Wire p. B at 15°. At start 0.239 ohm At start 0.247 ohm After heating red-hot: After several days in ) .. „ Twice in air at 1200° 0.238 " hydrogen at 15' Once in vacuo " 0.240 " After heating in hy- " "hydrogen" 0.262 " drogen to 1200° " "vacuo " 0.353 " Wire y. B at 15" At start 0. 183 ohm After heating in air to 1250° (three times) 0.182 " ■' H " " 0.188 " «' " ' " 0.195 " [ 0.255 86 HIGH TEMPERATURES. Wire y heated to 1350° in an earthenware tube and in hydrogen became brittle; this result may be explained by a siliciuration of the platinum, for there is nothing observed if the wire is heated by the electric current in the interior of a cold glass tube, even in hydrogen. Similar experiments were made by the same observers with palla- dium, rhodium, and iridium. With palladium the absorption of hydrogen at low tem- peratures, giving the hydride, increases the resistance by 60 per cent; besides, the same effect of alteration as with platinum is noticed if the palladium is placed in hydrogen in presence of silicium. There is no definite conclusion to be drawn from the experiments with rhodium and iridium, except that these metals assume their normal resistance only after having been heated several times to a high temperature. Law of the Variation of Platinum Resistance. — Cal- lendar and Griffiths have compared the resistance of platinum with the air-thermometer up to 550°; they found that up to 500° the relation could be represented at least to 0°.l by a parabolic formula of three parameters. In order to graduate such a pyrometer it would be sufficient then to have three fixed points : ice, water, sulphur. They gave a special form to the relation; let ^ be the electric temperature defined by the relation that is to say, the value of the temperature in the case in which the resistance varies proportionally to the tempera- ture. They then placed t . / M^ t-p, = 6 100 ' VlOO/ ELECTRICAL RESISTANCE PYROMETER. 87 It would appear as if this formula contained the single parameter 6; but in reality jt7t includes two. Substituting for p its value, we have Kt - K,t-r p^p .t-6 — poy^ . t , an equation of the form Rt = a + bt + ct\ This complicated form is without interest. Callendar and Griffiths used their pyrometer before having standard- ized it against the air-thermometer. Not being able to compute f, they provisionally computed the approximate temperatures pt^ and later determined the correction between t and p, , after having sought the formula express- ing the difference between these two quantities. By extra- polation up to 1000° the points of fusion of gold and of silver were found quite near to those determined by other observers. Holborn and Wien have shown, however, that at a high temperature the interpolation formula is certainly inexact. The resistance seems to become asymptotic to a straight line, while the formula leads to a maximum evidently inacceptable; it would be without doubt better represented by an expression of the form R.t =^ a + h{t -i- 273)™. Here are the results of several experiments made on the same wire by these two savants : t. R. t. R. Degrees. Ohms. Degrees. Ohms. 0.0355 1040 0.0356 1045 1510 1487 1193 1595 1699 1144 1574 1303 1338 1720 1395 1787 1425 1802 1518 1877 1550 1908 1578 1933 1610 1963 88 mas TEMPERATURES. This wire came in contact with the furnace-gases, as a result of breaking the tube, and was broken. Another wire gave the following results : t. B. 567° 0.0973 oj 772 1164 1045 1408 1185 1511 1363 1573 Experimental Arrangement (Fig. 14). — In Callendar's pyrometer the platinum wire is wound on two strips of ,^ mica set crosswise. Three heavy platinum wires serve to lead in and out the current; one of them is to compensate for the in- fluence of temperature along the parallel conductor. In the laboratory the resistance measure- ments are made by a Wheatstone's bridge (Fig. 15). A resistance-box is used, fur- nished also with a rheostat consisting of a stretched platinum wire serving to measure the small fractions of resistance. In industrial practice use is made of an apparatus (Pig. 15 his) composed of a needle- gavanometer and a resistance-box of cir- cular form, consisting of fifteen spools of 1 ohm. The deflection corresponding to two successive contacts is read, and by inter- polation is found the real value of the resist- ance. The approximation thus obtained is sufficient. To avoid breaking, the pyrometer should be installed in advance in the cold furnace, or heated previously in a muffle if it is necessary to Fig. 14. BLECTRIGAL RE8I8TANGB P7R0METBR. 89 introduce it into the hot furnace. It is necessary to take care and heat the porcelain throughout sufficient of its length in order to avoid the efiect of the interior con- ductibility, which would prevent the spiral taking the temperature of the surrounding medium. (^ (f) JB-^^^^i 1.8196 100° 102°. 5 565 2.7520 2.4500 3.010 ^ = (+2.5) 200 198.2 (-1.8) 1,260 3.1004 2.7984 2.397 400 405 (+5) 8,030 3.4814 3.1794 2.608 600 602 (+2) 4,920 3.6920 3.3900 2.780 800 800 (0) 6,970 3,8432 3.5412 2.903 1000 996 (-4) 9,080 3.9581 3.6561 2.998 1200 1208 (+8) 11,460 4.0591 3.7571 8.082 1400 1410 (+10) 13,860 4.1418 8.8398 3.150 1600 1603 (+3) 16,220 4.3100 3.9080 3.205 observations are suflBcient theoretically, it will be prudent in practice to utilize for the graduation a greater number of fixed points so as to have a check on the accuracy of the observations. The points whose use is to be recom- mended by reason of the accuracy with which they are known, and for their ease of use, are the following: Ebullition of water ; Ebullition of naphthaline or, in default, the fusion of tin; Ebullition of sulphur or, in default, the fusion of zinc; Ebullition of zinc or, in default, the fusion of gold; Fusion of platinum. The fusing-points are easier to use than the boiling- points at high temperatures; but their precision is slightly less. THBRMOELBGTRIO PTROMBTER. 121 For the boili.7ig-points of water, naphthaline, and sul- phur it is convenient to make use of an arrangement due to Barus (Fig. 23). This consists of a tube of thin glass, similar to test-tubes, of 15 mm. inside diameter, 300 mm. long, with a small bulb at 50 mm. below the open end. It is surrounded with a plaster muff of 150 mm. height and 100 mm. diameter which has been cast about the glass tube inside of a thin metallic cylinder forming the outside surface. The bulb is immediately above the plaster jacket, below which the tube, closed at its lower end, extends to a distance of 70 mm. As soon as the plaster has begun to set, the glass tube is taken out, giving it a slight twisting motion. The cylinder is left to dry, and the tube is again put in place. This allows, when the tube is broken, to take it out and replace it, which would be diflBcult if it adhered to the plaster. The lower free portion is heated by a Bunsen flame, gently at first, then without any special precaution, once boiling sets in. The liquid at rest should occiipy two- thirds of the height of the free end of the tube. The heating is continued until the liquid coming from the condensation of the vapor runs abundantly down the wallg of the bulb. The flame is then adjusted so that the limit of condensation of the liquid, which is very sharp, remains constantly midway up the bulb. There is then a perfectly uniform temperature in the interior of the glass tube throughout the height of the plaster cylinder. The junc- I^&. 23. 122 BIOS TEMPERATURES. tion of the couple is inserted and the coil of the gal- vanometer takes up a fixed invariable position.* For the boiling-point of zinc Barus made small cruci- bles of porcelain very ingeniously arranged, but also very complicated, besides being fragile and costly. One can make use more simply of a porcelain crucible 70 mm. deep (Fig. 24), filled with melted zinc for 50 mm. of its depth, and above, 20 mm. of charcoal-dust. A cone pierced with a central hole lets pass a small porcelain tube containing the couple. The whole is heated until there is seen a small white flame of zinc escaping from the crucible. It is indispensable that the openings for the escape of zinc vapor be large enough. They tend, indeed, to become clogged by a deposit of zinc oxide which solders at the same time the Fig. 24. cover to the crucible, and this causes an explosion when there is no longer vent for the zinc vapors. Use may be made to advantage for this heating, and still more for the heating of small crucibles to a very high tem- perature, of a furnace model of English make (Fig. 25), which has the advantage to resist almost indefinitely the action of heat and to be very easily repaired. The princi- ple of the construction of these furnaces is to make them of two concentric layers. The outer covering of fire-clay, bound together by iron, gives solidity to the furnace; it • It is well to prevent tUe liquid from running down about the couple by placing a small cone of platinum above the junction. — Tb. TEBBMOELBCTRIC PYROMBTEB. 123 receives but indirectly the action of the heat, and is not exposed to cracking by shrinkage under the action of too high temperatures. The inner envelope, which alone receives the action of the heat, is made of large-grained quartz sand, grains of 1 mm., mixed with a small amount of a flux. At a high temperature the quartz does not shrink as does clay; it expands, on the contrary, passing over to the form of amorphous silica with a change of density from 2.6 to 2.2. But this transformation is effected only with extreme slowness, otherwise it would burst the furnace. If by chance this inner lining falls down, it is easily replaced by putting into the furnace a glass jar of Fig. 25. suitable diameter, surrounded with a sheet of oiled paper, and packing about this, coarse quartz sand slightly moist- ened with a sirupy solution of alkaline silicate. The furnace is heated by means of a lateral opening with a Fletcher lamp, which has the advantage of being sturdy, or with an ordinary blast-lamp. In the use of fusing-points there are several cases to distinguish. If one wishes to employ a considerable quan- tity of metal, as with zinc, lead, and tin, the easiest way is to melt them in a crucible, into which is thrust the 124 HIGH TEMPERATURSa. properly protected couple and let the whole cool. There is observed with no difficulty the stationary temperature of solidification. If only a small quantity of metal can be employed, as in the ease of gold, or if there is no installation for heating the crucibles, it is possible to obtain the fusing-points as follows : One wraps about the junction, so as to cover it completely, a fine wire of the metal chosen (it sufiices with a little practice to use but a centigramme of metal), and then places the couple in an enclosure at stationary tem- perature slightly higher than that of fusion, or at tempera- ture increasing very regularly. The galvanometer readings are noted, which at the instant of fusion show a momentary halt followed by a sudden jump. But this perturbation is the more feeble the smaller the metallic mass, and a certain practice is necessary in this kind of observation in order to seize with certainty the halting-point. It is evident that the heating must be absolutely regular. It is im- possible to obtain this result with a free flame, which is always unsteady. In order to have a stationary tempera- ture, use is made in the laboratory of a tube or a muffle placed in a furnace that has been lighted for some time; at industrial works, a chimney or flue for the escape of smoke. In these enclosures the temperature varies from spot to spot, and one can, after a few trials, find the proper temperature. In order to work at increasing temperatures, which is the most convenient in the laboratory, the junction is placed, properly prepared, in a little crucible filled with powdered, non-fusible, poor conducting material, or else the junction is simply wrapped in a buUet of plaster, clay, or Purimachos. Care is taken to begin by drying and dehydrating slowly this bullet to prevent its bursting. It is then placed in a flame sufficiently hot to bring about fusion of the metal ; this flame should be very steady. THERMOELECmW PTBOMBTER. 125 For the fusion of platinum a different process should be followed. One utilizes the fusion of the wires of the couple in the same operation which serves to make the junction. Two observers are necessary, one to read the galvanometer and the other to note the fusion of the platinum. It is necessary to employ a flame sufficiently tall so that the temperature be regular throughout a con- Pt (1773°) p- E 80C / / / / / / / 1/ / / ny A '' / K ka) t / ^ / ^ 1 / / / [X / / (3) ^ ■y / // V ^ y / / / / / ^ / y /y 1 i 20 6 60 80 15 20 120 160 Au(io65?) Zn ^ q 3o ? ebulliUon) Al (BSS") S (Vi*8°) Zn(^20'' fusion) C'°H'(2l8°) H^Odoo?) IW ISOmTnfl) ^ 35 37,5 divisicms (2) 380 300 mm (3) Fig. 26. siderable height. The junction of the two twisted wires is placed at a distance of at least 50 mm. above the blast-lamp nozzle, a strong blast of oxygen is turned on, and the gas-cock is opened gradually until fusion takes place. The same process should be used for the fusion of gold, with an air blast-lamp, on the condition that the flame of 126 mOE TEMPERATURES. the latter be kept steady, which is not possible with bellows worked by foot. This method is, however, less precise than those that have been previously indicated. We give here the curves of graduation (Fig. 26) of different couples, attached to different galvanometers or, in the case of tho method of opposition (Poggendorf s method), to a PouiUet rheostat. In the last case the zero of graduation does not correspond to a zero electromotive force, and in consequence not to the temperature of the surrounding air, by reason of the supplementary resistance of a wire which was added to that of the rheostat. Fixed Mirror Pointer Method of Points. Galvanometer. Galvanometer. Opposition. Boiling water 100° 4.5 divs. Boiling naphthaline 218 12 " 2.5 divs. 13 mm. Melting zinc 420 26 Boiling sulphur 445 28 " 123 " Melting aluminium . 655 12 divs. Boilingzinc 930 64 294 " Melting gold 1065 30 divs. Melting platinum... 1780 137.5 divs. 37 "J Experimental Results. — The measurement of tempera- tures by thermoelectric couples has enhanced the accurate knowledge of a great number of high temperatures of which previously little or nothing was known. The measurements have been particularly numerous in the scientific and industrial investigations on iron. It is with the thermoelectric couple that Osmond and others, Robert Austin, Arnold, Howe, and Oharpy have made all their studies on the molecular transformations of irons and steels. The conditions of manufacture and of treatment of these metals have been improved by the introduction into industrial works of this method of high-temperature measurements. We give below, as examples, a series of determinations THERMOELEOTniC PYROMETER. 127 made by Le Chatelier in a certain number of industrial appliances. Steel. — Siemens-Martin furnace : Gas at the outlet of the gas-generator 730° Gas at the entrance of the recuperator 400 Gas at the outlet of the recuperator 1300 Air " " " " " " 1000 Interior of the furnace during refining 1550 Smoke at the foot of the chimney 300 Glass. — Basin furnace for bottles; pot furnace for window-glass : Furnace 1400° Glass in affinage 1810 Annealing of bottles 585 Drying of window-glass 600 Illuminating-gas. — Gazogtoe furnace : Top of furnace 1190° Base of furnace 1060 Retort at end of distillation 975 Smoke at base of recuperator 680 Porcelain. — Furnaces: Hard porcelain 1400° China porcelain 1275 Conditions of Use. — Thermoelectric couples by reason of their easy use and of the precision of their indications are preferable to aU other pyrometric methods for ordinary investigations, scientific or industrial, and in fact they are almost the only ones employed to-day for such uses. Their employment, however, is not to be recommended for investigations of the highest precision; the preference should be given, as we have already said, to the electric- 128 EIQE TEMPER AT VUES. resistance pyrometer * as soon as we possess the means to graduate it with precision up to high temperatures. From another standpoint one will be led to discard the thermo- electric couples when one does not possess a sufficiently skilful personnel to make the necessary small electric in- stallation, or when one shrinks from the expense of buying a galvanometer. * But see recent work at the Reichsanstalt on this point, especially regarding the evaporation of platinum at high temperatures. — Tb. CHAPTEE VII. HEAT-RADIATION PTROMETEK. 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 instrument by the body to be studied; this heat change is either a rise of temperature or a resulting phenomenon, such as a change of electrical resistance, 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. q — Kj^ — IC j^ — K JIj . ^2, d being the diameter of the radiating surface 8, E its emissive power. Now, — is the apparent diameter of the object; the quantity of heat radiated depends then upon the solid angle under which the object is seen. The emissive power E is very variable from one substance to another, and for the same substance variable with the 129 130 jiig:^ temperatures. temperature. It would be desirable to determine this, but that is difficult, often impossible, especially at high tem- peratures. The coeflacient Ic" is a function of the temperature alone, which expresses the law of variation of the radiation with the temperature. This law should be determined in the first place. It is on the more or less exact knowledge of this law that the entire accuracy of the results de- pends. The precision of the experimental measurements has not practically, as things are, other than a secondary importance. 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 now, the determination of the sun's tempera- ture, but they may serve other uses. Pouillet's Experiments. — Before PouiUet, Gasparin had already made some trials. His apparatus consisted of a hollow brass sphere mounted on a foot and blackened; a thermome- ter was used to measure the rise in temperature of the water contained in the sphere. The advantage of this arrangement was that the ap- paratus was always turned properly toward the sun. The pyrrMliometre of PouiUet consists of a calorimeter which meas- "1 Tires directly the heat received by "" " """"' radiation (Pig. 37). A very thin '^' " silver box is carried by a hollow tube, cut along a generatrix to let the thermometer be seen. HEAT-RADIATION PTROMETEB. 131 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 meant 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 orientation. To take an observation, the apparatus 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. PouiUet 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). PouiUet found by this method 1300° for the temperature of the sun. Experiments of VioUe. — 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. 28). 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 substi- tuted for water. The inner covering of 150 mm. diameter is blackened inside. The thermometer has a spherical 132 HIGH TEMPERATUBEB. bulb whose diameter varies from 5 to 15 mm. ; the surface of 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-glass Fig. 28. mirror slightly blackened, which permits of determining that the solar rays fall quite exactly upon the thermometer bulb. The establishment of the temperature equilibrium re- quires fif-teen minutes, and the difEerences of temperature observed vary from 15° to 20°. VioUe found in this way, for the temperature of the sun, figures varying from 1500° to 2500°. Pouillet and VioUe made use of Dulong and Petit's law of radiation, HEAT-RADIATION PYROMETER. 133 that the disooTerers had established by observations reach- ing 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 difEerent 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, 1 = corresponding to A. = 659 ; k = h " " A = 546; * = tV. " *' A. = 460. For very small objects which would have to be placed very near, a supplementary objective is put in front of the telescope; the object is placed in the principal focus of this new lens, the objective of the apparatus being focussed for parallel rays. The absorptive power of this supplementary lens is reckoned as ^ Details of an Observation. — The first operation to make is the determination of the absorption eoefiicients of the absorbing-glasses. For that, one views an object of suit- able intensity once with the tinted glass before the cat's- eye and then without this glass. Let W be the aperture of the cat's-eye without tinted glass, and N' the aperture with such a glass. The coefficient K of absorption is ■=&)■ The following observations furnish data for the deter- mination of the absorbing powers of different glasses employed in the course of studies relative to the radiations from incandescent mantles. Emissive Foioer. — Before being able to establish the relation which exists between the intensity of radiation of incandescent bodies and their temperature, it is necessary to know the emissive powers of these bodies. For this measurement use is made of the principle stated above, that the interior of fissures in bodies may be considered as enclosed in an envelope at uniform temperature. The emissive power is thus, at the temperature considered, 150 HIGH TEMPERATUBES. equal to the ratio of the luminous intensity of the surface to that of the bottom of deep fissures, with the condition, evidently, that the aperture of the fissures be suflQciently small. ABSORBING-GLASS PLACED BEFORE THE BOTTRCE TO BE STUDIED. Temperature. Aperture of Cat's-eye. Eed. Green. Blue. 1270° (+ 1 glass) 19.5 5.5 21.3 7.9 35 1870 (no erlass) 11 1 Ki. = 12.5 kg = 7.3 ki = 9.9 ABSORBING- GLASS PLACED BEFORE THE STANDARD LAMP. 1170° (- 1 glass). 1170 (no glass). . . 2.9 9.4 5.95 16.1 kr = 10.5 I S„ 7.3 10.2 31.5 ^6 = 9.5 The body to be studied was placed in the state of a paste, as dry as possible, on the end of a couple previously flattened so as to take the form of a disk of 2 or 3 mm. diameter. The drying was very slow, so as not to have any swelling of the mass, and one obtained in this way a coating possessing fissures; the conditions described above are then satisfied. The end of the couple thus prepared is heated either in a Bunsen flame or a blast-lamp, and the tempera- ture of the junction is noted, while, simultaneously, read- are taken with the optical pyrometer. In order to obtain a temperature as constant as possible, it is necessary to guard against currents of air and use a flame of small size. Here are some results obtained : Green. (1) (3) 21.0 14.0 Blue. (1) (8) 23.0 11.0 9.0 12.0 12.0 4.5 3.2 3.5 3.5 2.0 2.0 1.9 1.9 5.0 .... 4.0 L. 18.5 6.7 19.0 9.0 8.2 3.1 7.7 4.1 3.1 1.8 8.2 2.1 LUMINOUS RADIATION P7B0METER. 151 I. COtTPLE COVERED 'WTrH A MIXTUKE CONTAINING 99 PARTS OP THORIUM AND 1 OP CERIUM. Temperatures. ,,. ^"^ /2^ 950° (- 1 glass) 16.0 ... 1170 15.5 9.0 1375 7.0 3.0 1525 3.2 2.0 1650 (+ 1 glass) 8.3 6.0 n. MAGNEBIA. 1340° (- 1 glass) 12.2 4.0 1460 (- 1 glass) 4.9 2.5 1540 (- 1 glass) 2.4 1.3 The numbers give the divisions of the cat's-eye; those of column (1) refer to the surface, and those of column (2) to the bottom of the fissures. The indications (—1 glass) and (-|- 1 glass) mean that the absorbing-glass is placed either before the standard lamp or before the source studied. Jleasiiremefits of Intensity. — The following table gives an idea of the order of magnitude of the intensities of different luminous sources, the measurements of brightness being made in the red. Unity is the brightness of the axial portion of stearine candle-flame. Carbon beginning to glow (600°) 0.0001 Silver melting (950°) 0.015 Stearine candle, \ (xas-flame, >■ 1.0 Acetate of unyl lamp, ) Pigeon-lamp, with mineral oil 1.1 Argand burner, with chimney 1.9 Auer burner 2.05 FesO, melting (1350°) 2.25 Palladium melting 4.8 Platinum melting 15.0 Incandescent lamp 40 Crater of electric arc 10,000 Sun at midday , 90,000 152 HIGH TEMPERATURES. Graduation. — Le Chatelier made a first graduation of the optical pyrometer by measuring the brightness of iron 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 in which unit intensity corresponds to the most brilliant ) axial region of the flame of a candle. (7 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 given 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. 35. After having determined the value of the diaphragm d^ , which gives equality of brightness of the standard candle with that of the comparison-lamp, and the absorbing power fc of the tinted glasses, one may, as was said before, prepare LUMINOUS BADIATION PTBOMETBR 153 a table which gives directly the temperature corresponding to each aperture of the cat's-eye. C3 / 2,9 3 34 3,2 3,3 ^M 3,S 3,6 3,7 9.S 3^ k Log. ('.+273) Fig. 35. 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 lamp. This graduation applies to all bodies placed in an en- closure at the same temperature, in the interior of furnaces for example, and to black bodies whatever the temperature surrounding them, for example 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 neces- 154 man tempesatvres. sary, when they are exposed to the air and not surrounded by an enclosure at the same temperature, to make a special graduation. Temperatures. 700°.... 800 .... 900 ... . 1000 . . . . 1100 .... 1200 . . . . 1300 .... 1400 . . . . 1500 . . . . 1600 . . . . 1700 .... 1800 . . . . 1900 . . . . 2000 . . . . 2 Glasses. , 17.3 . 6.9 — Aperture of the Cat's-ey* 1 Glass. Glass. + 1 Gl lass. + 2 23.0 11.0 5.6 18.6 10.5 6.5 4.0 13. 9. 6. 4. 3. 13.0 9.1 7.3 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 (( + 873) h LogJ^ Iv Logi„ ^6 Logl^ 900° 3.0707 0.0009 4.95 0.00018 4.25 0.00003 5.3 1180 3.161 .0034 3.88 .0087 3.94 .0015 3.17 1275 3.190 .075 2.78 .037 2.57 .013 2.11 1430 3.230 .23 1.36 .16 1.67 .058 3.76 1565 3.265 .72 1.86 .47 1.20 .34 1.38 1715 3.300 1.69 0.23 1.45 0.16 .9 0.95 Evaluation of Temperatnres. — Finally, Le Chatelier has used his optical pyrometer to determine the very highest temperatures realized in some of the most important phenomena in nature or in the industries. These results. LUMINOUS RADIATION PYROMETER. 155 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° Furnace of glass-works 1375 to 1400 Furnace for hard porcelain 1370 " " new porcelain 1350 Incandescent lamp ■ 1800 Arc lamp 4100 Sun 7600 This determination of the temperature of the sun has been confirmed by the more recent experiments of Wilson and Gray (page 165) by a totally different method. A series of measurements were made with the same apparatus in iron-works. Here are some results : BLAST-FTJBNACEFOK BESSEMEB CASTING. Crucible before the blast-pipe 1930° Flow of the casting, beginning 1400 " " " " end 1530 BESSEMER CONVERTBK. Flow of the scoria 1580° " " " steel into the pocket 1640 " " " •• " " moulds 1580 Reheating of the ingot 1300 End of the hammering 1080 SrEMENS-MAETrN FUENACB. Flow of the steel into the pocket, beginning 1580° " " " " " " " end 1430 " into the moulds 1490 Conditions of Use. — The optical pyrometer, by reason of the uncertainty of emissive powers and of the shght sensi- bility of the eye for comparisons of luminous intensities, cannot give as accurate results as other pyrometric 156 HIGH TEMPERATURES. methodB. Its use should be limited to the cases in which other methods necessarily fail; 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 be much simpler and less costly, and to require no installation in a fixed position. It has, on the other hand, the inconvenience 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. 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- LUMINOm RADIATION PYROMETER. 157 eter. The table that he drew up is reproduced everywhere to-day : First visible red 525° Dull orange 1100° Dull red 700 Bright orange 1300 Turning to cberry 800 White 1300 Cberryproper 900 Melting white 1400 Bright cherry 1000 Dazzling white 1500 The estimation of these hues, 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. h. 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 variations 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 noticed in the first place that the ratio of the radiations transmitted varies with the thick- ness of the glass as well as their absolute intensity. Let /„ and I^ be the intensities of the radiations emitted, ka and Tc,, 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 ha is different from h^. It results from this that two cobalt glasses, differing in thickness or in amount of cobalt, will not give the same 158 EIOB TEMPBBATXTREa. 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 MesurS and Nouel. — It is known that by placing between two nicols a plate of quartz cut perpendic- ular to the axis a certain number of the radiations of the spectrum are suppressed. This latter is then composed of dark bands whose spacing depends on the thickness of the quartz and the position of the angle of the nicols. Mesure and Nouel have utilized this principle in order to cut out the central portions of the spectrum; this solution is excellent and preferable to the use of absorbing media. The appa- ratus (Fig. 36) consists essentially of a polarizer P and an Fig. 36. analyzer A, whose adjustment to extinction gives the zero of graduation of the divided circle GC. This circle is graduated in degrees and is movable before a fixed index I. Between the two nicols P and ^ is a quartz Q of suitable LUMINOUS BAVIATION PYROMETER. 159 thickness, carefully calibrated. The mounting M allows of its quick removal if it is necessary to verify thead just- ment of the nicols P and A. The quartz Q is cut perpen- dicularly to the axis. A lens L views the opposite opening C furnished with a parallel-faced plate glass or, where desired, with a dtffusing-glass very slightly ground. The relative proportions of various rays that an incan- descent body emits varying with the temperature, it follows that for a given position of the analyzer A the composite tint obtained is different for different temperatures. If the analyzer is turned while a given luminous body is received, 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 transition 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 iu one sense or the other from the type temperature. This is the ordinary method of use of this instrument. It is desired in a given manufacturing process (steel, glass) to make sure that the temperature of the furnace rests always the same; the instrument is ad- justed once for all for this temperature. It suSices to have but a short experience to train the eye to appreciate the direction of the changes of hue. The inventors have sought to make of their apparatus a measuring instrument; this idea is quite open to de- 160 BIOH TEMPERATURE8. bate. Intheory this is easy; it suffices, instead of having 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 tempera- ture the sensitive hue is slightly different, and it is im- possible to remember throughout the scale of temperatures the hues that were chosen on the day of the graduation. 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 : Temperature. An^le of Analyzer. Sun 8000° 84 86 Gas-flame 1680 05 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 remain always quite large. Pyrometer of Crova. — Crova has endeavored to give to the method of estimation of temperatures based on the unequal variation of different radiations of the spectrum a 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 have given more exact results than the preceding ones. The eye is much less sensitive to difference of intensity L UMINO US RADIATION PYROMETER. 1 6 1 than to difference of hue, so that there is no advantage to make use of observations of intensity. Crova compares two radiations, \ = 676 (red), X = 523 (green), coming from the object studied and from the oil-lamp used as standard. For this purpose, by means of a variable diaphragm, he brings to equality one of the two radiations emanating from each of the sources, and measures after- wards 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 usiug 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 (A. = 676 and X = 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 X = 523, and 65° 52' for X = 676. The instrument is then so adjusted that the dark band 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 radiation with the diaphragm, then, without touching the diaphragm again, one brings the green to equality by turning the nicol. 162 HIGH TEMPERATURES. The optical degree is given by the formula iV" = 1000 cos^ 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 N = — s— ) and the rotation varying from 0° to 90°, the cos^ 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 33°. 2. Complication and slowness of observations. It is diflBcult 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 requires about half an hour. 3. Absence of comparison in terms of the air-thermom- eter. 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. CHAPTEK IX. CONTRACTION PYROMETER (WEDGWOOD). 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 compar- able results, it would be necessary to prepare simultane- ously, under the same conditions, a great quantity of cylinders, 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 ^^ of -^-^ of an inch, or YTi'o incli) which corresponds to a relative contraction of -jTjVs" "^ Ta — Tw^ ^ terms of the initial dimensions. 163 164 man temperatures. We then have the following relation between the Wedgwood 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 90 182 Ao-gile de Mussidan 8 14 36 78 120 Limoges porcelain 2 21 88 91 Faience de Cboisy-le-Eoi. ... 2 5 12 48 75 Faience de Nevers 33 melted melted Kaolin 4 13 15 55 118 Clay 35> Titanic acid 75) \\ 4 9 19 123 160 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 cyhnders 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 metals made by Wedgwood, but the results are too dis- CONTBAOTION PTBO METER. 165 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 a hundred kilogrammes per square centimeter, in moulds of turned steel. The precision of the measurements is increased by augmenting 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 is not adapted for this graduation because the curve of contraction of clay in function of the temperature is too 166 HIGU TEMPERATURES. 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 yery 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 necessary 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. That would not be the case, however, for stanniferous 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. CHAPTEK X. FUSIBLE CONES (SEGER). A LONG time ago it was proposed to compare tem- peratures by means of the fusing-points of certain metals and alloys. But the non-oxidizable metals are not numer- ous and all are very costly : silver, gold, palladium, platinum. Use has, however, been made sometimes of these metals' and their alloys, in admitting that the fusing-point of a mixture of two substances is the arithmeiical 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 prefectly 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. 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 niatterS; that is to say, of mixtures containing an excess 167 168 HIGH TEMPERATURM8. 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 1883. 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 porcelain of Sevres. Seger, director of a research laboratory at the royal pottery works of Berlin, published, in 1886, an important memoir on this question. He determined 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: SiOj 46.9 A1,0 38.6 FeOa , 0.8 Alkalies 1.1 Water 12.7 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 (Pig. 37) is that of triangular pyramids of 15 mm. on a side and 50 mm. high. Under FUSIBLE CONES. 169 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 fiatten- FiG. 37. 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 described. 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 032; 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 kaolins and feldspars from different sources never have ex- actly 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 Al^Oj + lOSiO^. This is for the reason that this mixture is more fusible 170 HIOB TEMPEBATURE8. 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 page 173 giTes 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 Al^Oj. The cones 5 to 28 from the cone 5 by addition of in- creasing quantities of the mixture Al^O, + lOSiO^. 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 AljO, + 2SiOj. Fig. 38 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 aU intermittent furnaces whose temperature has to increase constantly up to a certain maximum, at which point the cooling-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 be watched. In seeing them fall successively, one Xnows at what moments the furnace takes on a series of definite temperatures. FUSIBLE CONES. 171 In continuous furnaces, the cones may be put into the furnace during the process, but that is more delicate. It tlWA +(l-x)(° 500' 0»+( SiO=)„,K«o\ Fig. 38. 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. 172 HIGH TEMPEBATURES. Dw. T. 38 1890 SB 1H50 SS 1830 M 1810 <^!^ 1790 u 1770 i\ 1TS0 m 1730 J9 1710 3 ( I . „.„ 10.06Fe^33f+'*^'°^ h 4SiO, I0.4A1,C, i 0.1 Fe^Os i0.2Fe2Os (■+ 4 010a 1 8.96 SiO. "•"jo.OSBjO . 1 3.90 Si o; lO.lOBjOs I J3.85SiO, "•"10.153303 ,j 3.80 SiO, "•"10.20830, I j 3.75 SiO. "•"lO.SSBiOs I J 3. 70 SiO- "•"I0.3OB3O3 ,j 3.65 SiO, "•" laasB.Oa , i 3.60 SiO. ■*"10.40B303 , J8.55SiOa "<"1o.45B303 I 13.5 SiO, "Mas B,0, Formulae. 9 1 79 58 X AljOj -Kl-X)(Al,O8-)-10SiO3) X{AI,0s -I- Cl- io SiO,) ^/0.3K,OI ■^^ 1,0.7 CaOf -|-0.5(Al,O3-|-10SiOa)) X fO.5 Al,Ps + 4 SiO,) + (1 -^).(0.5P'e,O -I- 4 SiO, + 0.7 CaO) ^(SiO, . BjOa) U<'-^)(S:??i8^ -I- l8:l#i;8!}+*sio,) FITSIBLE Q0NE8. 173 Nos. 920 Composition. X 0.61 FormulsB, Oil , ) 0.5 Na,0 ' \ 0.5 PbO [ + 0.8 AljOa-l- 8.6 SiO, 1.0 B,Oa 012 890 1 + 0.76 " +. 3.6 SiO, 1.0 BjOs 018 860 1 + 0.70 " +■ 3.4 SiOj 1.0 BjOs 3.3 SlOj 1.0 BjOs 014 830 1 ^* + 0.65 «' + 015 800 1 ** + 0.60 " + 3.2 SiOj 1.0 B-Oa 8.1 SlOj 1.0 BjjOs 0.57 X(2 SiOa + AI2O3) 016 770 1 ** + 0.65 " + +a-«(SiS&°[ 017 740 1 '* + 0.50 " 4- 3.0 SiO. 1.0 BjOs 2.8SiOj l.OBjOs 2.6SiOj l.OBjO^ +l?ifoU) 018 710 1 ** + 0.40 " + 019 680 jl " + 0.30 " + 020 650 1 " + 0.20 " + 2.4 SiOj l.OBjOa 021 620 1 '* + 0.10 » + 2.2SiO» l.OBjOs 022 590 1 " + j 2.0SiOj l.OBaOa CHAPTEK XI. BECORDING PYEOMETEES. AnoifG the diflferent methods for the measurement of high temperatures, some of them may be made contin- uously recording. This recording is as useful for industrial applications as for scientific investigations. In research laboratories one endeavors as much as possible to take observations automatically, escaping the influence either of preconceived ideas or of carelessness of the observer; in industrial works the use of su.ch processes gives contin- uous control over the work of the artisans, such as the presence of no foreman can replace. The record may be made by means of a pen or by photography. The former of these methods, more simple to handle, is preferable in works ; the second, whose indi- cations are more precise, is preferable in the laboratory. In general, however, one has not the choice, each phenom- enon utilized in the measurements being treatable by only one method of registering. So far, only three among the different pyrometers have been rendered recording: The gas-thermometer at constant volume; The thermoelectric pyrometer; The electrical-resistance pyrometer. But practically, up to now, the thermoelectric pyrometer alone has been used to take continuous records. Recording Gas-pyrometer. — The transformation of the gas-thermometer into a recording instrument is extremely 174 REOOBDINO PTR0METER8. 1^5 simple and has been long since effected. It suffices to join permanently the tube from the porcelain bulb to a regis- tering manometer to realize a recording pyrometer theoretically perfect. But practically these instruments possess many disadvantages that have prevented their in- troduction generally. Above 1000° the permeability of the porcelain for water-vapor is sufficient to soon render them useless. Investigations made by the Paris Gas Company have shown that in furnaces heated to 1100° the penetration of water- vapor is sufficiently rapid so that in a few days liquid water collects in the cold parts of the apparatus. Absolute impermeability of the apparatus, which is quite indispensable since its operation supposes the in- variability of the gaseous mass, is very difficult to obtain. Frequently the glazing of the porcelain has holes in it. The numerous joints entering into the registering appa- ratus, and above all the metallic parts of the apparatus, may be the seats of very small leakages difficult to locate. The connection of the metallic parts with the porcelain tube is generally made with wax, always with substances of organic origin which, in the vicinity of industrial appa- ratus, generally bulky and thick-walled, cannot be pro- tected against radiation save by a water-jacket. This is a serious inconvenience. In laboratory apparatus of small size the protection of the joint is easier, but then the large dimensions of the bulb, as has been indicated, are a serious disadvantage. One cannot, in a small furnace, find a large volume whose temperature is uniform. But the most serious disadvantage of the recording gas- pyrometer, and the principal reason for its abandon- ment, is the difficulty of its graduation. Already with the mercury-manometer the waste space is a source 176 HIGH TEMPERATVBES. of complications. However, this may be measured and allowed for. With the registering manometer the waste space is much greater, and besides variable with the deformation of the elastic tube. Thus the graduation can be made only empirically, employing baths of fixed fusing- or boiling-points, an operation almost always impossible of realization with an apparatus of very fragile porcelain. Fig. 39. Electrical-resistance Recording-pyrometer. — After the gas-pyrometer, the oldest, we shall describe immediately RECOBDINO PYROMETERS. 177 the electrical-resistance pyrometer, whicli is the most recent. It has not yet been used, and for this reason there is little to say regarding it. In order to render his pyrometer recording (Fig. 39), Callendar employs the following yery simple device. Two of the branches of a Wheatstone bridge used to measure the resistance of the heated coil are made of a single wire, on which slides a rider to which is brought one of the galvanometer leads. To each position of the rider, when the galvanometer is at zero, corresponds a resistance, and consequently a definite temperature of the coil. The posi- tion of the rider may be easily registered by attaching to it a pen writing on a sheet of paper which moves perpen- dicularly to the length of the wire. In order to have the curve thus obtained correspond to that of temperatures, it suffices that the position of the rider be at each instant ad- justed so as to keep the galvanometer at zero. This result is obtained by means of a clock-movement controlled by a relay that the galvanometer works in one direction or the other according to the direction of the deflection that it tends to take on from the zero-point. It is a movable-coU galvanometer whose needle carries an arm which, making contact, causes a current to pass. Fig. 40 gives an example of a curve recorded by this apparatus. This complicated registering apparatus is necessarily very costly, but it is actually the only one which effects the record of high temperatures by purely mechanical means, without the intervention of photography; it is possible that it will be used in certain large industrial works. For work in the laboratory it seems less convenient; the registering deprives the method of electrical resistances of the great precision which belongs to it and in which consists its great 178 EIGH TEMPERATURES. merit; there are also disadvantages such as the necessity to use for the protection of the coil a fragile tube of porce- lain of considerable volume. This recorder possesses an interesting detail which IgJIQfC. US09 iiBO^ xiem tlSO' assures good working and which could well be adopted in other similar cases. The pointer of the galvanometer- needle does not hit against a fixed conductor to which it would stick on account of heating by the passage of the current and especially the extra current at break. This conductor consists of the metallic circumference of a wheel which is given a slow constant rotary motion, rendering all adherence impossible. This artifice renders possible work- ing the relays by means of a sensitive galvanometer, which would not otherwise be realizable. Oallendar has applied the same method of recording to RECOBDING PTBOMETERa. 179 Langley's bolometer. The curve record of solar radiation for a day. of Fig. 41 gives the to It Midi: I Fig. 41. Theoretically, at least, the same method of recording may be applied to the measurement of temperatures by means of thermoelectric couples by using the method of opposition. But in this case the strength of the currents available to work the relays is much more feeble than in the preceding applications, and it is not certain that a sufficient sensibility can be obtained. Thermoelectric Recording-pyrometer, — The only re- cording-pyrometers currently in use to-day are the thermo- electric pyrometers recording photographically. Numerous attempts have been made to secure a recorder with a pen, as is done in the case of the recording-voltmeters and ammeters in use industrially, but, up to the present, with- out success. The strengths of current which can be utUized are too weak; for a precision of 10° an apparatus sensible to ^^Xt,!^ volt is necessary; the resistance of the galvanometer-coUs should be considerable, 100 ohms at least, as has been previously explained, and the correspond- ing current will be only a millionth of an ampere. There are on the market such alleged recording-pyrometers, but they are constructed with galvanometer-coUg of but few 180 HlflH TEMPERATURES. ohms' resistance and >rannot give measurements of tem- perature exact to 100°.^ For the recording of temperatures one may seek two quite different results, to which are appropriate two methods of recording equally different. One may desire to deter- mine the temperature at a definite epoch, that is to say, to trace the temperature curve in function of the time. This will be almost always the object in view in industrial works. It suffices, in this case, to let fall the luminous beam reflected by the galvanometer-mirror on a sensitive plate possessing a vertical movement of translation. The two coordinates of the curve thus recorded give, the one tem- perature, the other time. One may desire, on the other hand, to know the rate of variation of the temperature at a given instant, and at the same time the corresponding value of the temperaturo. This is the case in the greater number of laboratory investigations in which is desired the temperature at which a definite phenomenon occurs: fusion, allotropic transformation, etc.; and in order to recognize the occurrence of this phenomenon, use is ordi- narily of the accompanying absorption or liberation of latent heat, which is manifested by a variation in the law of heating or of cooling. It is this latter method of recording that Le Chatelier first developed during his investigations on clays. A luminous beam reflected by the galvanometer-mirror falls periodically at regular intervals, of a second for instance, upon a fixed sensitive plate. The distance apart of two successive images gives the variation of temperature during unit time, that is, the rate of heating or of cooling; the distance of the same image to the image corresponding to the beginning of the heating will give the measurement of the temperature. In all cases of photographic recording it is necessary to REOOBDING P7B0METERS. 181 replace the ordinary galvanometer-mirrors, which give images quite insufficient as to definition and brightness, by special mirrors made of a plane convex lens, silvered on the plane surface. These mirrors are slightly heavier than parallel-face mirrors, but have two important advan- tages : the absence of extra images reflected by the front surface of the mirror, and a greater rigidity which obviates accidental bendings of the mirror arising from the attach- ments to its support. One may easily get good mirrors of this type of 20 mm. diameter, and with more difficulty of 30 mm. diameter. These last give nine times more light than the mirrors ordinarily employed. It is easy to so choose the lens as to give a mirror of desired focal length. A plane convex lens whose principal focus by transmission is 1 m. will give, after silvering the plane surface, an optical system equivalent to a parallel-faced mirror whose radius of curvature would be 1 m. Discontinuous Recording. — In this manner of recording the luminous source should possess periodic variations; one of the simplest to employ is the electric spark between two metallic points. The interruption of the current is produced by a pendulum at definite intervals of time. In order to have a spark sufficiently bright, it is neces- sary to use an induction-coil so worked as to give freely sparks of 50 mm., and to reinforce it by a Leyden jar which reduces the length of these sparks to 5 mm. ; it suffices for this to use a jar of 1 to 3 liters. The choice of metals for the points is equally important; zinc, aluminium, and especially magnesium give sparks that are very photo- genic. These metals possess the disadvantage of oxidizing quite rapidly in air, so that it is necessary from time to time to clean the points with a file. The metallic sticks may have 5 mm. diameter, and the distance apart of the points is % mm, One might without doubt, using mercury, 182 HIGH TEMPERATURES. which gives sparks as photogenic as does magnesium, con- struct an enclosed apparatus in which the metal would be preserved unchanged. To produce the interruption there is attached to the pendulum (Fig. 43) a vertical platinum fork which dips into two cups of mercury covered with alcohol. It is useful, in order to reduce to a minimum the resist- ance that the immersion of the fork opposes to the motion of the pendulum, to place this fork in the same horizontal plane as the axis of rotation of the pendu- Olum. In this way one avoids the translatory movements in the mercury which cause the most Fig. 43. trouble. The only refinement with this intermittent lighting is to obtain, with a spark much too large and irregular to be photographed directly, the illumination of a very narrow slit. It is not sufficient to place the spark behind the slit and at a small distance away, because the slightest displace- ment of the spark would cause the luminous beam to fall outside of the mirror of the galvanometer. This difficulty -y Fig. 43. is overcome by a well-known artifice. A lens is placed between the electrodes and the mirror (Fig. 43) ; the posi- RECORDING PYROMETERS. 183 tion of the electrodes is so adjusted that the image of the mirror is formed between them. With a distance apart of the electrodes of 2 mm., a lens of 100 mm. focal length and a mirror of 25 mm. diameter, the image of the latter will touch the two points; the spark then necessarily crosses the image of the mirror, and the radiations passed by the lens will fall certainly upon the mirror. One is thus sure in placing before the lens a fine metallic slit that all the rays transmitted will reach the mirror and will be sent to the photographic plate, and that whatever may be the position of the slit in front of the lens. To save time it is advantageous to take several sets of observations on the same plate; this is easily done by arranging the plate so that it may be displaced vertically between two series, or in adjusting the slit so that it may be moved similarly before the lens. The diagram (Fig. 44) is the reproduction of negatives H,0 S Se Au BO^ foo° *l»8t 665? lo45? t H riHU'llllllllillllllllllli I lllliniBd INI !(lll!lilllllllli|lliBilJil IliJ IIIIIHIIIIIIIIiillllMlllllllllllllllllllllllliJB^^^^^^^^^^^^ I :|IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIMIIIIIIIIIIIIIIII||||||lll!l||||IIBill| iiiiiiiiiiiiniMniiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiim^^^^^^^^^^ iiiiiiiiiiiiiiiiiii!!!r''?ji5^s lllllllll 1 1 1 1 1 1 1 1 1 1 1 1 II I 111 lllllllllllllllll!llliaiillllillllil!l!illlll!illllll!llllllllt^^^ Fig. 44. relative to the action of heat on clays. The first line gives the graduation of the couple; it has been drawn from SCA eral different photographs which have been grouped to economize space. The following lines are reproductions of negatives made in phototypography without any inter- vention of the hand of the engraver. The second line, for example, represents the heating of an ordinary clay. A slight contraction of the lines between 150° and 350° indicates a first phenomenon with absorption of heat; 184: SIGH TEMPEUATUBES. it is the vaporization of the enclosed water. A second cooling much more marked between 550° and 650° shows the dehydration properly so called of the clay, the libera- tion of the two molecules of water in combination. Finally, the considerable spacing of the lines at 1000° . shows a sudden setting-free of heat corresponding to the isomeric change of state, after which the alumina becomes insoluble in acids. The other rows refer to the heating of other varieties of clay, the third row to kaolin, the fifth to steargilite. Continuous Recording. — The continuous recording of temperatures is of much more general usage, even in scientific laboratories, by reason doubtless of the greater simplicity of its installation. It has been studied especially by Eoberts Austin, director of the royal mint at London. A vertical slit lighted from a convenient source projects its image, by means of the galvanometer mirror, on a metallic plate pierced by a fine horizontal slit, and behind this slit moves a sensitive surface, plate or paper, which receives the luminous beam, defined by the intersection of the horizontal slit with the image of the vertical slit. If all were at rest, the impression ijroduced by this luminous beam would be reduced to a point. If the plate alone is moved, a vertical straight line will be had; if the gal- vanometer mirror alone turns, a horizontal line. Finally, the simultaneous displacement of the plate and mirror gives a curve whose abscissas represent temperatures, and whose ordinates time. The illumination of the slit and the motion of the sensitive surface may be realized in many different ways. Lighting of the Slit— There are two quite distinct cases to consider, that of laboratory researches by rapid heating or cooling, which last only a few minutes, and that of con- tinuous recording of temperatures in industrial works, BEOORDINQ PYROMETERS. 1S5 which may last hours and days, that is to say, periods 100 times to 1000 times longer. The rate of displacement of the sensitive surface, and consequently the time of exposure to the luminous action, may vary in the same ratio. The luminous source necessary will be therefore quite different, depending upon the case. For very slow displacements it is sufficient to use a small kerosene lamp with a flame of 5 to 10 mm. high. For more rapid displacements use may be made of an ordinary oil- lamp, an Auer burner, or an incandescent lamp ; finally, for very rapid displacements of the sensitive plate, 10 mm. to 100 mm. per minute, one may advantageously employ the oxyhydrogen flame or the electric arc. For oxyhydrogen light the most convenient is the lamp of Dr. Eoux with magnesium spheres; it con- sumes little gas and is enclosed in a metallic box which prevents all troublesome diffusions of the light. The electric arc gives much more light than is needed, and the rapid wearing away of the carbon, by displacing the positions of the luminous point, ren- ders difllcult the permanence of suitable illumination of the slit. For very short experiments one may very conveniently use the mercUry-lamp in vacuo (Fig. 45) ^ or the arc playing between two mercury surfaces. In- order to run it 3 amperes at 30 volts are requisite. Its only disadvan- tage is to go out after running a few minutes on account of the evaporation of the mercury in the central tube, suffices, it is true, to give it a slight jar to make it go again, by causing a small ^"*- ^^• quantity of mercury to pass from the outside annular space into the central tube. Whatever the luminous source employed, the slit may s ew I 186 BIGH TSMPBBATURES. be always lighted by means of a lens arranged as was indicated for discontinuous recording, that is, projecting upon the galvanometer mirror the image of the luminous source. When this is large enough, it suffices to place the slit before the luminous source, bringing it up close enough so as to be sure that some of the luminous rays passing through fall upon the mirror. But there is danger here of so heating considerably the slit that it may be altered; for this reason one is led to use more voluminous light-sources than would otherwise be necessary. In the case of the use of a lens, the useful luminou.s intensity is as great as in placing the slit immediately next to the luminous source, so long as the image of the latter is greater than the gal- vanometer-mirror; now with the ordinary dimensions of the sources employed this condition is always fulfilled without any special precaution. Instead of a slit lighted by a distinct luminous source, use may be made of a platinum wire, or better, as does Charpy, employ a carbon filament of an incandescent lamp heated by an electric current. In order that the line traced by the recorder be very fine, it is necessary that the two slits, the luminous slit and the horizontal slit, be equally fine. Skilful mechanicians can cut such slits in metals. But it is easier to make them by taking a photographic plate of bromide-gelatine that has been exposed to the light, developing until com- pletely black, then wash and dry. By cutting the gelatine with the point of a penknife guided by a ruler, one may get transparent slits of a perfect fineness and sharpness. Sensitive Surface. — For sensitive surfaces use is made of plates or films of bromide-gelatine. Professor Eoberts Austin employs exclusively plates which permit more easily the printing of a great number of positive proofs. Charpy, in his researches on the tempering of steel, made BEOORDING PTROMETEBS. 187 use of sensitive paper, which permits a much more simple installation. Paper. — For industrial recording, paper would allow of the employing large rolls lasting several days, as in the recording magnetic apparatus of Mascart. But in general one wants to have quickly the results of the record; this is always the case in laboratory investigations, and almost always in industrial studies. It is thus preferable to be content with quite short bands of paper rolled on a cylinder. There exists such a model quite well known and easy to use : the recording-cylinders with an interior clock-movement of the firm Kichard. They may be ordered from the maker with any desired rate of rotation; unfortunately this rate cannot be changed at the pleasure of the operator, a desideratum in laboratory investiga- tions. Fig. 46 represents the installation of the recording- pyrometer used by Charpy in his researches on the temper- ing of steel. To the right the galvanometer, to the left the Eichard recording-cylinder, and in the middle the electric furnace used for heating the samples of steel. 188 HIGH TEMPERATURES. Plates.- — The plate may be placed in a movable frame regulated by a clock-movement; this is the first arrange- ment employed by Prof. Eoberts Austin (Fig. 47). But Fig. 47. this installation, somewhat costly and complicated, has the same disadvantage as the recording-cylinders in that but a single speed can be given to the sensitive surface. In order to drive the plate Eob- erts Austin now uses a buoyed sys- tem in which the rate of rise of level of the water is controlled at will by the agency of a Mar- iotte's flask and a simple water- cock. The plate is. kept in an invariable vertical plane by means of two lateral cleats whose fric- tion is negligible on account of the mobility of the float. The Pj^ ^g sketch (Pig. 48) gives the arrange- ment of a similar apparatus made by Pellin for the laboratory of the College de France. RECOBDINO P7R0MBTBR8. 189 It carries a 13 x 18 cm. plate which is attached to the float by means of two lateral springs not shown in the sketch. Neither are the two guides of the float, immersed in water, indicated; the play next the cleats is only two- tenths of a millimeter. The uncertainty that this play can cause in the position of the plate is quite negligible. The curve (Pig. 49) is the reproduction of an experiment made with such an arrangement by Koberts Austin on the solidification of gold. 1065? c 12?C. Pro. 49. During the whole period of freezing, the temperature remained stationary, then lowering of temperature was pro- duced at a regularly decreasing rate as the temperature of the metal approached that of the surroundings. It is indispensable to trace on each sensitive surface on which is to be recorded a curve, the line corresponding to the surrounding temperature, or at least a parallel refer- ence line. This is very easy in the case of the guided plate or of the paper rolled on a cylinder. It suflBces, after having brought the couple to the temperature of its surroundings, to displace in the opposite direction the 190 BIOS TEMPERATURES. sensitive surface; the second curve traced during this inverse movement is precisely the line of the zero of the graduation of the temperatures. But this is a dependence that may be evaded by registering at the same time as the curve a reference line by means of a fixed mirror attached to the galvanometer in the path of the luminous beam which lights the movable mirror. Roberts Austin likewise makes use of the luminous beam reflected by the fixed mirror to inscribe the time in a precise manner. A movable screen driven by a seconds pendulum cuts off at equal intervals of time this second luminous beam. The reference line, instead of being continuous, is made up of a series of discontinuous marks whose successively corre- sponding parts are at intervals of one second as is shown in Fig. 49. The curves once obtained must be very carefully ex- amined to recognize the points where the gradient presents slight anomalies, characteristic of the transformations of the body studied. Generally these irregularities are very insignificant, and it would be well, in order to recognize them with certainty, to obtain curves traced on a much greater scale. Practically this magnification is not possible; one may increase the sensitiveness of the galvanometer, and thus the defiection, but then for the greater range of temperature the luminous image would fall off the sensitive plate. Prof. Eoberts Austin has over- come this difficulty in an ingenious manner. He no longer registers the temperature of the body, but the difference between this temperature and that of a neighboring body which presents no transformation, platinum for instance. This difference of temperature, always small; may be recorded by a very sensitive galvanometer. If, at a given moment, the body, other than the platinum, undergoes a change of state accompanied by heat phenomena even very BECOBDING PTS0MMTEB8. 191 weak, the difference of the two temperatures, by reason of its small value, will undergo variations relatively very Fig. 50. great. If it is desired not merely to recognize the exist- ence of a phenomenon, but besides to measure the tem- PlG. 51. perature at which it is produced, it is necessary to employ simultaneously a couple connected to another galvanom- eter. With three leads, two of platinum and one of platinum-rhodium, a complex couple may be made, giving 192 BIOH TEMPERATURES. simultaneously the actual temperatures and the differences of temperature of two neighhoring hodies. The diagram (Fig. 50) gives an idea of this arrangement ■which has proved very useful in the hands of Koberts Austin for the study of alloys, and particularly for the study of the transformations of irons and steels. The curve of the solidification of tin is reproduced in Fig. 51, as obtained by this method. The double inflection indicates the exist- ence of marked under-cooling; the tin, before freezing, is lowered to 2° below its fusing-point, to which it returns suddenly as soon as solidification sets in. Eecording-pyrometers have been for the most part em- ployed up to the present only in scientific laboratories. There exist, however, a few in metallurgical works, as the blast-furnaces at Clarence Works of Sir Lothian Bell and the blast-furnaces of Dowlais. The curves of Fig. 52 give 700" \ 600: 40O°C ^' V r\ / ^ \ X- r-N 1 / A V / \ / v/ \. ^ / \ / \ 1 Fig. 53. an example of the curves obtained at Clarence Works • the lower curve gives the temperature of the gas at the fur- nace-mouth, and the upper curve that of the hot blast. CHAPTEK XII. CONCLUSION. In closing this account it will not be useless to call the attention of investigators to points whose study seems the most needed to aid the progress of our knowledge of high temperatures. We will mention first the precise deter- mination of the fixed points serving for the graduation of pyrometers; there does not exist at the present time above the boiling-point of sulphur any temperature known certainly to 1°. For the ebullition of zinc, the fusing of silver and that of gold, which are at present the best known, the uncertainty may be 10°. It would be well also to try and find substances serving for fixed points that are more convenient to handle than the metals — salts, for example — which do not attack platinum either when they are melted or when they are vaporized; these substances should be found easily and economically in a state of purity; they should possess well-defined points of fusion and of ebullition, which is not always the case when the crystallized salt has several dimorphous varieties. A second very important point for investigations of great precision would be the determination of the general form of the function which connects electrical resistance with temperature. One cannot hope to determine com- pletely this function with the value of its parameters, because there are not two samples of platinum having 193 194 HIGH TEMPERATURES. exactly the same resistance; it is necessary in each case to make the calibration by means of fixed fusing- or boiling- points. The number of such points to compare depends on the number of parameters contained in the formula. By his researches in this matter. Prof. Silas Holman has greatly facilitated the use of thermoelectric couples by showing that it is suflBcient between 0° and 1800° to use a logarithmic formula containing only two parameters. For the measurement of exceedingly high temperatures which can be effected only by methods employing radiation, and depending upon extrapolations often considerable, it wo aid be very useful to determine with greater precision, than has been done as yet, the law of the radiation from a rigorously black body (enclosed space), either for a monochromatic radiation, as radiation transmitted by the red glasses, or for the totality of heat radiations. But such a study can be of value only on the condition of pos- sessing a very great precision, difficult to attain actually on account of the uncertainty which still exists as to the temperatures directly measurable. For a moderate pre- cision the formulse of Stefan and of Le Chatelier will do, as they are certainly very near to the truth, since they are sensibly in agreement up to the temperature of the sun, about 8000°. It will certainly be necessary to verify and determine more accurately the parameters which enter into these two formulae. In closing we beg to call attention to a fact of some importance. The measurement of high temperatures possesses certainly great interest from the point of view of the progress of pure science; but it is to be noted that in- dustrial needs have stimulated the partial solution of this problem: Wedgwood, the china manufacturer, seeking to better his processes; similarly, Leger, at the Berlin works, CONCLUSIOK. 195 occupied himself exclusively with ceramic products; Siemens sought to regulate the making of steel; the engineers of the Paris Gas Company wanted a means of control over the distillation of oil; Le Chatelier studied the thermoelectric pyrometer in the course of investiga- tions on the baking of clay and on the manufacture of cements; he studied the optical pyrometer at the request of a Shefi&eld steel manufacturer, Hadfield, who desired for his works a pyrometer uniting accuracy with simplicity of use. Eoberts-Austen, director of the mint at London, has devoted all his efforts for many years past to the study of industrial alloys, obtaining results of great value, largely due to the utility of the recording-pyrometer. This incentive of practical needs on the progress of science is not surprising. The savants who founded chemistry recognized no distinction between pure and applied science. Lavoisier, Chevreul, Gay-Lussac, Dumas, Thenaud, H. Sainte-Glaire-Deville went indtEEerently into the laboratory or the works. It is the present trend of our teaching methods that has opened a breach increasing in size every day between theory and practice. In the scientific laboratories all efforts follow in well- beaten paths. There one is free to choose his subjects of study according to his caprices; one may be easily guided by artificial preoccupations, concerning themselves but very indirectly with a study of nature. Finally, one may have confidence for a. long time in erroneous results with- out having any inkling of the error committed. In in- dustrial works it is quite otherwise: one cannot remain stationary upon problems already solved; in spite of one's self one must march ahead. Subjects of study obtrude and must necessarily be taken up in the order of their real importance. Wrong conclusions are made evident by their contradictions at each instant with facts that one cannot 196 HIGH TEMPERATURES. refuse to see. These conditions explain how laboratories attached to industrial works, with their insufficient per- sonnel absorbed largely in other matters, with their rudi- mentary material, come nevertheless to contribute largely to the progress of pure science. AH the progress so im- portant in the chemistiy of iron is made to-day in indus- trial works and in the laboratories attached to them. It is not in chemistry alone that practical needs have manifested this creative power. It was in studying the boring of cannon that Eumford met the notion of the conservation of energy; it was in reflecting upon the steam-engine that Sadi-Carnot established the basis of thermodynamics; it was in seeking to perfect light-house lenses that led Fresnel to his investigations on the theory of light. CHAPTER XIII.* RECENT DEVELOPMENTS. As several important pyrometric investigations have been finished the past year, since the appearance of the French edition of this work, it may not be out of place to call attention to some of the advances that have been made. Gas-pyrometry. — It is now generally agreed that for temperatures above 300° C. it is advisable to use nitrogen as the thermometric substance. Hence a knowledge of the behavior of this gas is of prime importance. Ohappuis and Harker, working at the International Bureau at Sevres, have investigated anew the relation between the thermometric scale of the nitrogen-thermometer at con- stant volume, under an initial pressure of 800 mm., and the normal scale of temperatures from 0° to 500°. The expression for the dilatation of nitrogen at t° deduced from observations with their thermometer, under a pressure of 1 meter of mercury at 0° C, is P = 0.00367698 - 7.836746. 10-^ ^ -f 4.78007610-1". i!^ and their observations indicate the existence of a limiting value of this coeflBcient (i.e., supposing nitrogen to rest a perfect gas to 0° abs.) y^u^, = 0.00367380, * Written hj the translator, 197 198 HIGH TEMPEBATURBS. and as the mean coeflBcient of dilatation between 0° and 100° A-.00 = 0.00367466. The divergences of the nitrogen-thermometer from the normal scale were found to be as follows : Differences of Scale. Temperatures. Actual Scale — Normal Scale. Pg = 1 meter. • 100° 0°.000 150 -0 .008 200 -0 .017 250 -0 .036 300 -0 .034 350 -0 .043 400 -0 .051 450 -0 .060 500 -0 .068 Thus up to 500° C. the divergence of the nitrogen con- stant-volume scale from the normal scale is very slight, and appears to be of less account than other sources of uncer- tainty. This divergence is further lessened with smaller values of the initial pressure {P^; and is less than 0°.04 at the sulphur boiling-point, for a value of P^ =^550 mm. The divergence of the nitrogen constant-volume ther- mometer from the normal scale of temperatures in terms of the initial pressure leads to the expression -J- = 1.33 . 10-* per mm. change of pressure. op For very low initial pressure this gives ySum. = 0.0036613. For hydrogen • \"^= 0.0036625 | according to Ber- ■^ ^ ■ I Am. = 0.0036634 \ thelot. For high temperatures the constant-pressure form is probably more accurate and convenient (Barus, Chappuis, RECENT DEVELOPMENTS. 199 Callendar). For nitrogen under constant pressure Chap- puis gives -r — = 1.19 . 10-* per mm. - and «uin. = 0.0036612. The divergences from the normal scale in this case are about double those at constant volume. Callendar suggests that probably helium will eventually be used in defining the normal scale of temperatures. An extended study of the constant-volume thermometer has been made by Holborn and Day at the Eeichsanstalt, Berlin. They find that for work up to 500° C. a more suitable substance for the thermometer-bulb than porcelain is a ha'rd borosilicate glass, Jena 69™; that porcelain should not be used at all; and that for temperatures above 500° a platin-iridium bulb filled with pure nitrogen at an initially low pressure gives entirely satisfactory results and is easy to handle. A great improvement over the older methods of heating for all temperatures is the use of an electric oven made of nickel wire wound upon a thin tube of porcelain or clay and suitably enclosed. Their form of gas-thermometer is almost identical with that of Chappuis. They determined also, among others, the following ex- pansion coefficients per unit length at 0° : Jena 591" - x- 18.10"' from 0°-100° Porcelain : X = (3954J + 1.125<«)10 - » from 0°-1000° Platinam : X = (8868* + 1.324<')10 - » from 0°-1000° Palladium : X = (8198< + 1.418«')10 - » from 0°-1000° Silver . X = (18370«-|- 4.793i')10 - « from 0°-875° Nickel : X = (13460<-|- 3. 315««)10 -» from 300°-1000° Pt— 10!? Ir : ^ = (8889< + 1.374<2)10 -9 from 0°-1000° Pt— 30^ Ir : ;i = (8198ii + l.418i:')10 " » from 0°-1000° 200 HIGH TEMPERATURES. Eegarding the absolute value of temperatures as- deduced by comparison with the gas-pyrometer, the following quotation from Barus * is to the point : "If, as is undoubtedly true, platinum is impermeable to nitrogen at dull-red heat and at white heat, we witness finally the solution so long deferred of the pyrometric problem, at least for the lower region of high tempera- tures. We are grateful to our predecessors for the data they have left us, but it is expedient to lay aside all their work and to endeavor to obtain entirely new results by means of new apparatus clearly freed from systematic errors. The Eeichsanstalt is to be congratulated for having taken the first step in this direction." Thermoelectric Pyrometer. — As the thermoelectric couple has come into such general use, the importance of ready and accurate calibration is apparent. If the couple is to be used over only a short range of temperature, interpolation in the Avernarius formula is suflBcient, the determinations of two known fixed points being required. For more extended ranges of temperature this formula may be replaced to advantage by the Holman logarithmic formula : 2*e = mt". The two constants are readily computed or evaluated graphically, and the resulting plot serves indefinitely for the determination of any temperature with a given couple. The equation loses in precision below 250° 0. It may be written log 2*e = n log t + log m, * Tr. of Report to Physics Congress, Paris, 1900. RECENT DEVELOPMENTS. 201 and if log '2*e is plotted as abscissas and log t as ordi- nates, the resulting curve is a straight line. Unfortu- nately, in the experimental work of Holman, Lawrence and Barr, they assumed the value of the melting-point of gold as 1072° (Holborn and Wien). Taking the now best- known value of this point, 1064° (Holborn and Day, D. Berthelot), and for the boiling-point of sulphur 445°, the application of this formula gives the following values of the melting-points that they determined : Al Ag Au Cu pt 654.7 962.7 [1064] 1087 1760 If we compare these values with those recently obtained by Holborn and Day at the Eeichsanstalt : Al Ak Au Cu * 657.3 961.5 1064 1084 made by means of a thermo-couple in direct comparison with the gas-thermometer, and bearing in mind that Holman did not use an electric heater, we see that his formula may be applied in all confidence to the determina- tion of high temperatures in ordinary practice. For the calibration of the couple, the boiling-point of sulphur (445°) and the melting-point of copper (1064°. 9 in an oxidizing atmosphere or 1084°. 1 in a reducing atmosphere) are amply suflBcient and easily obtained. For an accuracy of ± 1° C, Holborn and Day have shown that above 250° 0. the following formula holds within wide limits : 2*e= -a-\- U+ct^ and they have employed it in their recent researches. The labor involved in computation with this form is con- siderable, and unless a very great accuracy is required * For measurements in a graphite crucible a. slightly lower value was found. 202 SIGH TEMPEUATURBS. Holman's formula is amply sufl&cient, when the uncertainty of the absolute values of high temperatures is considered. Stansfield deduces from theoretical considerations the formula which may be written E^aT-{-l\og T+c, a form which satisfies the experimental results determined with pure platinum wires. This form possesses no prac- tical advantage over that of Holborn and Day, unless it be its usefulness, by employing the graphical method, in detecting slight errors in fusing-points. The values of dE -r=f, at the points of fusion can be obtained from the T vs. (IT ^ E plot, and the T vs. -^ curve thus constructed throws into prominence the experimental errors at these points. As the above formula indicate, the curve for the platinum J rr metals constructed with T as abscissas and T. -rr^ as dT ordinates is a straight line. The errors of the method are less than 3° at 1000°. The ordinary metals, on the other hand, give nearly a straight line for the curve T vs. -^-^ Stansfield worked with Austen^s recording-pyrometer, which he has rendered still more sensitive by means of an auxiliary potentiometer, which balances the major part of the E.M.F. of the couple, the sensitive galvanometer being acted upon by only a small fraction of the thermo-current. The "cold'' junction was kept in boiling water. He obtained the following fixed points: Zinc Aluminium Silver Gold Copper 418'.3 649°.3 96r.5 1062°.7 1083°.0 ttEOBNT DEVMLOPMENT^. 203 After having calibrated several couples with their new platinum gas-pyrometer, Holborn and Day determined a series of boiling- and fusing-points of certain metals and alloys, obtaining very concordant results : Cadmium 321°.7 ± 0°.l (From 10 observations on two days.) Lead 326 .9 ± .3 " " " " " Zinc 419.9 ±0.3 Antimony 630 .5 ± .3 Aluminium.. . 657.5 ±0.5 (In a graphite crucible, a lower value.) Silver 961 .5 ± .9 (Pure; i.e., in reducing atmosphere.) Silver 955 (In air; point ill defined.) Gold (samp. 1) 1064 .0 ± .6 Gold (samp. 3) 1063 .5 (Crucible method.) Gold (samp. 3) 1063 .9 (Wire method.) Copper 1064.9 (In air.) Copper 1084 (Pure.) Their " wire method " is to insert into the circuit at the hot junction a centimeter of the wire whose melting-point is to be determined, and to note the E.M.F. at the instant the circuit breaks, due to the fusing of this wire. Only 0.03 gr. of gold are necessary to take an observation for that metal. As is evident from the table, the wire and crucible methods give identical results. The crucible may be of porcelain or graphite. From a consideration of the work of Holborn, Stansfield, and Holman it is evident that, working under most diverse experimental conditions with different thermo-couples of pure metals, lesults are obtained agreeing to 0.5 per cent or even closer. The work of Holborn and Day practically makes the thermo-element independent of the gas-ther- mometer, for platinum can be obtained to-day in a state of great homogeneity and purity, giving always the same E.M.F. at the same temperature, unless having been exposed to furnace-gases at temperatures above 1300°; and there are a number of "fixed points" known to 0.3 per 204 BIOH TEMPERATURES. cent within the range 200° to 1400°. In work oi con- siderable precision it is well to have at least two thermo- elements, one being kept as a standard, heated only in porcelain tubes and never higher than 1200° C. If the platinum of the couple has become nnhomo- geneous by excessive heating and the E.M.F. thus changed, the couple may be restored very nearly to its original con- dition and E. M. F. by heating to white heat for some time by the passage of a current (Holborn and Day) or by heating the wire wound on a refractory-earth cylinder (Bams). Platinum-resistance Pyrometer. — For the exact deter- mination of temperatures from the lowest to 700° or 800°, this pyrometer gives by far the most accurate results, whether it be a question of measuring a long range of temperature or controlling the constancy of "a temperature. It is currently in use in England to measure temperatures above 1000° where great accuracy is desired, but without warrant, for the recent researches of Tory only emphasize those of Holborn and Wien that even pure platinum changes considerably its "zero" by uncertain amounts when heated to 1000°, whether annealed or not, even when care is taken to shield the metal. To determine a temperature by means of a platinum- thermometer it is necessary to know the "difference coeflBcient," d, of the wire; or the difference between the "platinum temperature" of the given wire and that of a standard at any known temperature, as the sulphur boiling- point or the silver freezii.g-point. Callendar has suggested the following notation which has come pretty generally into use : Fundamental Interval = the denominator R' — R" in the formula pt = 100{R - BO)/{R' - RO), ... (1) BBCBNT DEVELOPMENTS. 205 for the platinum temperature pt, represents the change of resistance of the thermometer between 0° and 100°. Fundarhental Coefficient = c — mean value of tempera- ture coeflBcient of change of resistance between 0° and 100°: c={R' - J?»)/100 BP. Fundamental Zero = pt" = — = reciprocal of funda- mental coefficient. It represents the temperature on the scale of the instrument itself at which its resistance would vanish. Difference Formula. — The following form is the most convenient for computation : D^t-pt=d. {t/100 - 1) . t/100. . . (2) Parabolic Function expresses the vanishing at 0° and 100° of above formula, which becomes t=pt + d.p{t). " S.B.P." Method of Reduction. — D is obtained very conveniently by determining R", and thus pt" at t" — the boiling-point of sulphur. Resistance Formula. — The parabolic difference formula is equivalent to assuming R/I^=l+at + M\ .... (3) where a = c{l + d/100), 5 = - cd/10000. Graphic Method of Reduction. — The easiest way to reduce platinum temperatures to the gas scale is to plot the difference t — pt in terms of t as abscissas, and to deduce graphically the curve of difference in terms of pt as abscissas. This is most convenient for a single instru- ment up to 500°. 206 BIOS tempebaturss. other methods have been used by Heycock and NeTiUe and by Tory. Difference Formula in Terms of pt : t-pf^d'{pt/100-^)pt/100 = cl'p{pt). . (4) This formula is to be used only where a high degree of accuracy is not required. The value of d' may be deter- mined from S.B.P., or approximately d' =^d/{l - 0.077d). Dickson has proposed the formula {R + ar=p{t+b), which agrees with (3) over a very wide range in the case of platinum. It has the possible theoretical advantage of not requiring a maximum value for the resistance of platinum. This form, however, does not lend itself to the convenient graphical treatment applicable to the difference formula. There is advantage in using the silver fusing-point in calculating the value d for impure wires that are to be used at high temperatures. For the whole range of tempera- tures with such a wire both the sulphur and silver points may be obtained, when d takes the form a -f- it. The platinum-thermometer may be, and should be, constructed so as to read directly in platinum degrees. This method saves much time and chance of error. The calibration curve once made for a given instrument serves indefinitely, so that, in spite of the appearance of compli- cations in the method, actually in practical use the determination of a temperature on the normal scale by the platinum-thermometer is the affair of a few seconds only. " With regard to portability and ease of reproduction, it is sufficient to send a few grammes of the standard wire in RECENT DEVELOPMENTS. 207 an ordinary letter, to reproduce the scale with the utmost accuracy in any part of the world." Ohappuis and Barker have redetermined the sulphur boiling-point with a platinum-thermometer compared with the nitrogen-thermometer at the International Bureau at Sevres. Their result is 445°. 2, as compared with Callendar and Griffiths' value, 444°. 53, determined some years ago. Besides the reasons given by Ohappuis (difference in coefficient of bulbs, etc.), cumulative evidence seems to indicate that 444°. 53 is too low a value for this point. For instance, assuming this value, the platinum-thermom- eter gives 1061° as the fusing-point of gold. The best determinations made independently of the sulphur point, Holborn and Day, and D. Berthelot, both give 1064° for the gold point. If the boiling-point of sulphur be 445°. 0, then the platinum-thermometer also gives 1064° as the gold fusing-point. The change in S. B.P. suggested by Ohappuis corre- sponds to a change in c? of the difference formula from 1.500 to 1.538. Oallendar has strongly urged the adoption of the platinum-pyrometer as a practical or secondary standard to be used independently of the air-thermometer by com- paring all platinum-thermometers to one selected as standard, assuming values of the sulphur and silver points, 444°. 5 and 963° respectively. Fixed Points.— In the following table are grouped the most reliable recent determinations of the fixed points that may be used to advantage in pyrometry. Those put in brackets are the least exactly known or are difficult to determine experimentally. Radiation Pyrometers. — In Germany at the present time very extensive researches are being carried on to determine and verify the laws of radiation, especially of 208 HIGH TBMPEItATVRBS. 03 =3 o "o, « lis a a finlz; CO CO ^CD »0 50 CO CD 00 C»03000 «00 CC CO asc<) UDOO CD CO 03 CQ t-C^OiO w ir-H OS O 1^ 05 « lO CO CO « W T-( C4 -«# « «CO CO ■* CD CD CD CO 090 H« ^ !=! ot O e o CD CD 050 -CScD g oi Eh o 3 a <1 f=l O \, and c is a constant. The following table indicates the limits within which (1) holds. The results are those of Lummer and Prings- heim, obtained with various radiating substances and a strip-bolometer. The temperatures are expressed in terms of Holborn and Day's platinum-bulb nitrogen-thermometer as compared with a thermo-element. Nos. 5, 8, and 9 probably owe their divergences to the fact that they were obtained with a Perrot furnace at low temperatures and heat equilibrium was not realized. Froin the table it is evident that (1) is satisfied between the temperatures of 100° and 1300° 0. 210 HIGH temperaturt:8. C.lOl" Absolute Calculated robs.— rc t^os. Temperature. Temperature. 1 127 373M 374°. 6 - r.5 2 124 492 .5 492 .0 + .5 3 124.8 723 724 .3 - 1 .3 4 126.6 745 749 .1 - 4 .1 5 (116.7) 789 778 .0 +11 .0 6 121.6 810 806 .5 + 3 .5 7 123.3 868 867 .1 + .9 8 (115.9) 1092 1074 +18 9 (116.3) 1113 1095 4-17 10 124.2 1378 1379 - 1 11 123.1 1470 1468 + a 12 120.9 1497 1488 + 9 13 122.3 1535 1531 + 4 Mean 123.8 Assuming Stefan's law to be true, Wien and later Thiessen and Planck developed theoretically the expression A. !7'=const., (2) from which follow A„. T= const. -A, .... (3) E^. r-= = const. =B, .... (4) where A„ is wave-length of maximum energy at tempera- ture T, and E„ is the energy of A^. The following confirmation of (3) and (4) was obtained by Lummer and Pringsheim: A„ Era A = Xr^T B=E,n.T-^ Absolute Temperature. -. DifE. 4.53 2.026 2814 2190.10-" 621°.2 62r.3 ' + OM 4.08 4.28 2950 2166 723 721 .5 - 1.5 8.28 13.66 2980 2208 908.5 910.1 + 1.6 2.96 21.50 2956 2166 998.5 996.5 - 2.0 2.71 84.0 2966 2164 1094 5 1092 .3 - 2.2 3.35 68.8 2959 2176 1259 .0 1257 .5 - 1.5 2.04 145.0 2979 2184 1460 .4 1460 .0 - 0.4 1.78 270.6 2928 2246 1646 1653 .5 + 7.5 Mean.,.. 2940 2188.10"" RECENT DEVELOPMENTS. 211 The small difEerences among the values of A are within the limits of precision with which it is possible to deter- mine A„. The agreement among the values of B, which depend on the fifth power of T, is very satisfactory, bear- ing in mind also that above 1000° the temperature is de- termined by extrapolation in Holborn and Day's formula. Two other series of observations, with different arrange- ment of apparatus in each case, gave values for A of 3940 and 3930, and equally satisfactory constancy for B. Paschen has also made a long series of careful investiga- tions on this matter. He makes use of two methods : one, measurements on cavities of various kinds with heated walls; and the other, of the radiation of the black body by the method of reflection. The mean of his latest results for A reduced to Holborn and Day's scale is 3930 with a mean error of 16. Wanner also obtains A = 3930. Wien also deduced as the expression for the total energy of radiation of a black body E-CX-h"'^ (5) Cand c are determined from A and B of (3) and (4). A slightly modified form, due to Planck: E= CX-'-^, (6) e>^T _i is found by Paschen to hold more generally than does the Wien energy formula. For very long waves these formulae apply with less exactness, and also at high temperatures the value of A is slightly higher than at low temperatures, according to Paschen. For most substances heated to incandescence the value of X^T is on the average 3630, instead of 2930 as in the case of a "black" body. Therefore, without knowing the 212 HIGH TEMPERATURES. "blackness" of the surface in question, its temperature may be approximately found as being surely between two well-defined limits, when A^ is known for the body. In the formula . — * E=CX e '^r « = 6 for platinum and a — 5 for a l^lack body, and in general it is safe to take 6 > a > b. Lummer gives the following values calculated in this way, supposing the bodies to be "platinum-black": ^m ■'- max. -^ min. Electric arc 0.7// 4300° abs. 3750° abs. Nernsfslamp 1.2 2450 2300 Auerburner 1.3 2450 2200 Incandescent lamp 1.4 3100 1875 Candle 1.5 1960 1750 Argand burner 1.55 1900 1700 Other Pyrometers. — Mercury in glass thermometers reading up to 575° are now obtainable. The glass is Jena 59"' or a similar hard one, and the instrument is ftlled under great pressure, nitrogen usually occupying the stem above the mercury. A vacuum jacket sometimes surrounds the upper part of the stem to eliminate uncertain stem- exposure corrections. Dufour has succeeded in constructing a tin in quarz pyrometer permitting measurements from 340° to consid- erably above 1000°. If such pyrometers could be made commercially they would be useful, as such an instrument has no zero lag and is direct-reading. Wiborgh of Stockholm has on the market a "thermo- phone" suitable for the discontinuous determination of temperatures. It consists of a cylinder of refractory earth, 2.5 cm. long and 3 cm. in diameter, containing an explosive. The thermophone is deposited in the region whose temperature is to be ascertained, and the time is REGENT DEVELOPMENTS. 213 noted to one-fifth second until the cylinder explodes. A table then gives the required temperature. Different cylinders of the same set agree to one-fifth second, or 30° at 1000°. These thermophones are more convenient than, and as cheap and accurate, as, the Soger cones. Conclusion.* — The actual state of pyrometry is most encouraging. It is clear that in a few years from now pyrometry wiU be in possession of a series of constants as exact as those of the best developed branches of Physics. In Germany, a gas-thermometer impermeable to the thermometric gas and rigid up to white heat has been found, thanks to the efforts of Holborn, Wien, and Day, at the Eeichsanstalt. In England, the efforts of Cal- lendar, Griffiths, and others to construct an instrument of remarkable sensibility from the absolute zero to 1000° C. have been crowned with merited success. In France, the best practical pyrometer has been found by Le Chatelier, and D. Berthelot has devised an optical method for the measurement of temperatures in absolute value, independent of the form and size of the thermomet- ric envelopes, and whose upper limit is indefinite; for since we have learned, thanks to the great discovery of Nemst, that the refractory earths become conductors at high tem- peratures, it has become possible to heat electrically the most infusible substances up to the highest degrees on the scale. With a thermostat of this kind, Berthelot's pyrometric method in absolute value marches side by side with the most advanced practical progress realized by Moissan; in other terms, pyrometry in absolute value is only limited to-day by the difficulty of the manufacture of apparatus in refractory materials. * Barus : Report to Physics Congress, Paris, 1900, BIBLIOGRAPHICAL INDEX. (The italic figures refer to volumes.) NORMAl, SCALE OF TEMPERATURES. Carnot. — Reflections on the motive power of fire. LippmoMn. — Thermodynamics, p. 51. Thomson and Joule. — Philosophical Transactions of the Royal Society, 42 (1862), p. 579. Lehrfeldt. — Philosophical Magazine, 45 (1898), p. 363. Callendar.—Phil. Trans., 178 (1888), pp. 161-220. Begnault. — ^Account of his investigations, 1 (1847), p. 168. Chappuis. — Studies of the gas-thermometer. Trav. du Bureau International des Poids et Mesures, 6 (1888). Chappuis and Harker. — Trav. et Mem. du Bureau Int. des Poids et Mesures, 1900. Phil. Trans., 1900. Scftre&er.— Absolute Temperature. W. Beibl., 22 (1898), p. 297. GAS-PYROMETERS. Prinsep.— Ann. Chim. et Phys., 2d Series, U (1829), p. 247. Pouillet. — Treatise on Physics, 9th ed. (1858), 1, p. 233. — Comptea Rendus, S (1836), p. 782. Ed. Becquerel.—C. R., 57 (1863), pp. 855, 902, 955. Sainte-Glaire-Deville and Troost.—C. R., 90 (1880), pp. 727, 773; 45 (1857), p. 821; 49 (1859), p. 239; 56, p. 977; 57 (1863), pp. 894, 935; 98 (1884), p. 1427; 69 (1864), p. 162.— Ann. Chim. et Phys. (3), 58 (1860), p. 257.— R6pert. Chim. Appl. (1863), p. 326. TioJZe.— Specific heat of platinum. C. R., 85 (1877), p. 543.— Speeilio heat of palladium. C. R., 87 (1878), p. 98; 89 (1879), p. 702.— Boiling-point of zinc. C. R., 94 (1882), p. 721. 815 216 BIBLIOGRAPHICAL INDEX. Barus.—BuW. U. S. Geological Survey, No. 54 (1889) ; Phil. Mag. (5), Slf (1892), p. 1.— Report on Pyrometry, Congress at Paria, 1900. RegnauU. — Account of his experiments, 1, p. 168 (Paris 1847); M6m. de I'Institut, 21 (1847), pp. 91, 110; Ann. Chim. et Phys. (3), 68 (1861), p. 89. Holhorn and Wien. — Bull, de la Soc. pour I'encouragement (5), i (1896), p. 1012; Wied. Ann., ^7 (1892), p. 107; 46 (1895), p. 360.— Zeits. fur Instrum. (1892), p. 257. Crafts and Meier. — Vapor density of iodine. C. E., 90 (1880), p. 690. Jolly. — Pogg. Ann., Jubelband (1874), p. 97. Randall. — Permeability of platinum. Bull. Soc. Chim., 21 (1898), p. 682. Mallard and Le Chatelier. — Ann. des Mines, i (1884), p. 276. J. R. Erskine Murray. — On a new form of constant-volume air- thermometer, Edinburgh Proic., 21 (1896-97), p. 299, and Journ. Phys. Chem., 1 (1897), p. 714. J. Rosse-Innes. — The thermodynamic correction for an air-ther- mometer, etc. Nature, 58 (1898), p. 77.— Phil. Mag. (5), 45, (1898), p. 227; 50 (1900), p. 251.— Proe. Phys. Soc. London, 16 (1), (1898), p. 26. Chappuis.—Phi\. Mag. (5), 50 (1900), p. 433.— Report for Paris Congress, 1900.— Jour, de Phys., Jan. 1901, p. 20. D. Berthelot. — On a, new method of temperature measurement. C. R., 120 (1895), p. 831. Holbom and Day. — Wied. Ann., 68 (1899), p. 817, and Am. Jour. (4), 8 (1899), p. 165; Zeitschr. Instrum., May 1900.— Am. Jour. (4), 10 (1900), p. 171, and Drude's Ann., 2 (1900), p. 505. Chappuis and Barker. — Trav. et M6m. du Bureau Int. des Poida, etc., 1900; Phil. Trans., 1900. Callendar.—Fhil. Mag., 48 (1899), p. 519. CALORIMETRIC PYROMETER. Violle. —BoHing and fusing points. C. R., 89 (1879), p. 702. Le Chatelier. — Sixteenth Congress of the SociStS technique de I'in- dustrie du gaz (June 1889). Euchene. — Thermal relations in the distillation of oil. (Mono- graph.) BIBLIOGRAPHICAL INDBX. 217 BerifteZo*.— Calorimetry. Ann. Chim. et Phys., 4th Series, 20, p. 109; 5th Series, 5, p. 5; 5th Series, 10, pp. 433, 447; 5th Series, 12, p. 550. ELECTRICAL-RESISTANCE PYROMETER. W. Siemens.— Vtoc. Royal Soe., i9 (1871), p. 351.— Bakerian Lecture, 1871. — Transactions of the Society of Telegraph Engi- neers, 1879. — British Association, 1874, p. 242. Miiller. —Vogg. Ann., lOS (1858), p. 176. Benoit.—C. R., 76 (1873), p. 342. Callendar.—PUl. Trans, of R. S., 178 (1888), pp. 160-230; Proc. Roy. Soc. London, 4I (1886), p. 231, and Phil. Trans., 1887.— Phil. Trans. (1892), p. 119 (^vith Griffiths) .—Platmnm pyrome- ters. Iron and Steel Institute, May 1892.— Phil. Mag., 32 (1891), p. 104; 33 (1892), p. 220.— Proposals for a, standard scale of temperatures. B. A. Report, 1899; Phil. Mag., ^7 (1899), pp. 191, 519, is a rfisumS of the question. Heycock and Neville. — Determination of high temperatures. J. of Chem. Society, 68 (1895), pp. 160, 1024. Barus.—Amer. Jour. (3), 36 (1888), p. 427. Eolbom and TTiera.- Ann. der Phys. u. Ohem., ^7 (1892), p. 107; 56 (1895), p. 360.— Bull, de la Soc. d'encouragement, 5th Series, 1 (1896), p. 1012. Chappuis and Harker. — ^A comparison of platinum and gas-ther- mometers made at the B. Int. des Poids et Mesures. B. A. Report, 1899. — Trav. et Mem. du Bureau Int. des Poids et Mesures, 1900; Phil. Trans., 1900; Jour, de Phys., Jan. 1901. Appleyard.—Fhil. Mag. (5), 4I (1896), p. 62. Dickson.— Phil. Mag. (5), U (1897), p. 445; i5 (1898), p. 525. Wode.— Wied. Beibl., 23 (1899), p. 963; Proc. Cambr. Soc, 9 (1898), p. 526. OhrusteJww and Sitnikow. — Tagebl. d. russ. Naturf. Vers, zu Kiew (1898), p. 438. THERMOELECTRIC PYROMETER. Becguerel.—Ann. Chim. et Phys., 2d Series, 31 (1826), p. 371. Pouillet.—'VraXU de Physique, 4th Ed., 2, p. 684.— C. R., 3, p. 786. Ed. Becquerel. — ^Annales du Conservatoire, 4 (1864), p. 597. — C. K., 218 BIBLIOQRAPEICAL INDBX. 55 (1862), p. 826.— Ann. de Chim. et de Phys., 3d Series, 68 (1863), p. 49. Toi*.— Trans. Roy. Soc. Edinb., 27 (1872-73), p. 125. Regnault. — ^Account of investigations on heat-engines, 1, p. 240. — C. R., 21 (1847), p. 240. Enott and MacGregor.—Trms. Roy. Soc. Edinb., 28 (1876-77), p. 321. Le Chatelier. — ^Tbermoelectrie pyrometer. C. R., 102 (1886), p. 819. — Journal de Phys., 2d Series, 6, Jsun. 1887. — Genie civil, March 5, 1887. — 16th Congress of the Soci6t§ technique de I'industrie du gaz, June 1889. — Bull, de la SoeiStfe de I'en- couragement (1892).— Bull. Soc. Chim. Paris, 47 (1887), p. 42. Barus. — Washington, 1889, Bull, of the U. S. Geological Survey, No. 54, No. 103 (No. 54 contains a very complete historical account of the whole subject of pyrometry). — Phil. Mag. (5), Si (1892), p. 376.— Am. Jour., 36 (1888), p. 427; 47 (3), (1894), p. 366; 48, p. 336. Holborn and Wien.—Wied. Ann., 47 (1892), p. 107; 56 (1895), p. 360. — Zeit. des Vereines deutscher Ingenieure, 4^ (1896), p. 226.— Stahl und Eisen, 16, p. 840. Roierts-Attsten. — Recent progress in pyrometry. Trans. Am. In- stitute of Mining Engineers, 1893. {See also Recording Pyrometers.) Quincke. — Ceramic insulators for very high temperatures. Zeit. der Vereins deut. Ingenieure, 40, p. 101. Struthers. — Thermoelectric pyrometer of Le Chatelier. School of Mines Quarterly, New York, 12. E. Damour. — Bull, de 1' Assoc, amicale des anciens 6l6ves de I'Ecole des Mines (March 1889). H. ffowe.— Pyrometric data. Engineering and Mining Journal, 50 (1890), p. 426. Holborn and Day. — On the melting-point of gold. Drude's Ann., ^ (1), (1901), p. 99; Am. Jour, of Sci., 11, Feb. 1901, p. 145.— On the thermoelectric properties of certain metals. Sitz. Berl. Akad. (1899), p. 69; Am. Jour, of Sci. (4), 8 (1899), p. 303; Mitth. Phys.-tech. Reichsanst., 37 (1899). StansfieU.—'Phil. Mag. (5), 46 (1898), p. 59. Bolman.—Phil. Mag., 41 (1896), p. 465; Proe. Am. Acad., 31, p. 234. Eolman, Lawrence and Barr. — Phil. Mag., 4^ (1896), p, 37; Proe.. Am. Acad., 31, p. 218. BIBLIOaUAPHICAL INDEX. 219 Scnoentjes.—Aioh. de Phys. (4), 5 (1898), p. 136. Noll. — ^Thermoelectrieity of chemically pure metals. Wied. Ann., 1894, p. 874. SfeiwwaMre.— Thermoelectricity of certain alloys. C. R., ISO (1900), p. 1300; 131 (1900), p. 34. BeZZoc— Thermoelectricity of steels. C. E,., ISl (1900), p. 336. HEAT-RADIATION PYROMETER. Tiolle. — Solar radiation. Ann. Chim. et Phys., 5th Series, 20 (1877), p. 289.— Jour, de Phys. (1876), p. 277. BoseiM.— Ann. Chim. et Phys., 17 (1879), p. 177.— Phil. Mag., 8 (1879), p. 324. Deprez and d'Arsonval. — Socifitg de Physique, Feb. 5, 1886. Boj/s.- Radiomicrometer. Phil. Trans., 180 (1887), p. 159. Wilson and Qray. — ^Temperature of the Sun. Phil. Trans., 185 (1894), p. 361. Langley. — Bolometer. Am. Jour, of Science, 21 (1881), p. 187; 31, (1886), p. 1| 32 (1886), p. 90; (4), 5 (1898), p. 241.— Jour, de Phys., 9, p. 59. Terreschin. — Diss. St. Petersburg, 1898. Jour. Russ. phys.-chem. Ges., 29 (1897), pp. 22, 169, 277. Lummer and Kurlbaum. — ^Verh. phys. Ges., n (1898), p. 106. Petravel.—'PToe. Roy. Soe., 63 (1898), p. 403. ABBo*. — Bolometer. Astrophys. Jour., S (1898), p. 250. BeJZoc- Bolometer errors. L'gclair. elec. (5), 15 (1898), p. 383. LUMINOUS-RADIATION PYROMHFER. Kirchoft.— Ann. Chim. et Phys., 59 (1860), p. 124. Ed. Becquerel. — Optical measurement of temperatures. C. R., 55 (1863), p. 826.— Ann. Chim. et Phys., 68 (1863), p. 49. TioIIe.— Radiation from platinum. C. R., 88 (1879), p. 171; 91 (1881), pp. 866, 1204. Crom.—C. R., 87, pp. 322, 329; 90, p. 252; 92, pp. 36, 707; 114, p. 941; 126, f. 1394. Le CteteZier.— Optical pyrometer. C. R., 114 (1892), p. 214; J. de Phys., 3d Series, 1 (1892); Industrie 61ectrique, April 1892.— On the temperature of the sun. C. R., 114 (1892), p. 737. — On the temperatures of industrial furnaces. C. R., 114 (1892), p. 470. 220 BIBLIOGBAPEtCAL INDEX. Stefan.— Wien. Ber., 179 (1879), p. 391. Boltzmann.—Wied. Ann., 22 '(1884). Paschen.—Wied.. Ann., 60 (1897); Astrophys. Jour., 10 (1899), p. 40; 11 (1900), p. 288. C. E. Mendenhall and Saunders. — ^Aatrophys. Jour., IS (1901), p. 25. Lummer. — Report Phys. Congress, Paris, 1900: Radiation from black bodies. Lummer and Pringsheim. — ^Wied. Ann., 63 (1897), p. 395. — Verb. d. Deutsch. Phys. Ges., 1 (1899), pp. 1, 12; 2, No. 5 (1900). ^lanck.— Tirade's Ann., 1, Nos. 1, 4 (1900). Wien.— Ber. der Berl. Akad., 6 (1893).— Report Phys. Coi^ess, Paris, 1900: Laws of Radiation. Kurlbaum.—Wied. Ann. 67 (1899), p. 846. CONTRACTION PYROMETER. Wedgvxiod.—Phil. Trans., 72 (1782), p. 305; 74 (1784), p. 358. Guyton and Morveau. — Ann. Chim. et Phys., 1st Series, ^6 (1803), p. 276; 73 (1810), p. 254; H (1810), pp. 18, 129; 90 (1814), pp. 113, 225. J. Joly. — ^The melodometer. Proc. Roy. Irish Academy, 3d Serie^ 2 (1891), p. 38. Ramsay and Eumorfopoulos. — Phil. Mag., il (1896), p. 360. FUSIBLE-CONE PYROMETER. Lauth and Togt. — Pyrometric measurements. Bull. Soc. Chim. J(6 (1886), p. 786. Se^er.— Thorindustrie Zeitung, 1885, p. 121; 1886, pp. 135, 229. RECORDING PYROMETERS. he Chatelier.—S,tudj of clays. C. R., 104 (1887), p. 1443. Roberts-Austen. — First Report of the Alloys Research Committee, Proc. Inst. Mech. Engrs. (1891), p. 543.— Nature, 45 (1892).— B. A. Report (1891).— Jour, of Soc. of Chem. Industry, 46 (1896), p. 1.— Proc. Inst. Mech. Eng. (1895), p. 269; (1897), pp. 67, 243.— Proc. Roy. Soc, 49 (1891), p. 347. G. Charpy. — Study of the tempering of steel. Bull, de la Soc. d'encouragement, 4th Series, 10 (1895), p. 666. BIBLtOOttAPHIOAL INDEX. 221 Callendar. — Platinum recording pyrometer. Engineering, May 26, (1899), p. 675. Stansfield.—F'hil. Mag. (5), 46 (1898), p. 59; Phys. Soc. London, 16 (2), (1898), p. 103. BristoJ.— Air-pyrometer. Eng. News, Dec. 13, 1900. FUSING AND BOILING POINTS. Prinsep.— Ann. Chim. et Phys., 2d Series, U (1829), p. 247. Lauth.— Bull. Soc. Ohim. Paris, 46 (1886), p. 786. E. Becquerel.— Ana. Chim. et Phys., 3d Series, 68 (1863), p. 497. 7iolle.—C. R., 85 (1877), p. 543; 87 (1878), p. 981;| 89 (1879), p. 702. Holiom and TFie«.— Wied. Ann., 47 (1892), p. 107; 56 (1895), p. 360; also Zeits. fur Instrumentenk. (1892), p. 257. Eolbom 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. — Jahrls. fUr das Berg, und Huttenw. im K. Sachsen (1879), p. 154. Le(fe6oer.— Wied. Beib., 5 (1881), p. 650. Tan der Weyde. — 1879, see Carnelley's Tables. Callendar.— Phil. Mag., 5th Series, .^7 (1899), p. 191; 48, p. 519. Curie. — Ann. de Ohim. 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. BertJielot.—C. R., 126, Feb. 1898. Le Chatelier.—C. R., 114 (1892), p. 470. T. Meyer, Riddle and Larrib. — Chem. Ber., 27 (1894), p. 3129. (Salts.) Moldenke. — ^Zeita. fur Instrumentenk., 19 (1898), p. 153. (Iron and Steel.) OMSOcfc.— Proc. Roy. Irish Acad., 3d Series, 4 (1899), p. 399. Landolt and Bornstein. — Phys. Chem. Tabellen, Berlin, 1894. Carnelley. — Melting and Boiling Point Tables, London, 1885. Bolman, Lamrence and Barr.—PHl. Mag. (5), 42 (1896), p. 37, and Proc. Am. Acad., SI, p. 218. &22 SiBLtOGMAPBlCAL INDBX. Beyeoch 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. EBULLITION. Bants. — h. C. (under Fusion), and Am. Jour. (5), 48 (1894), p. 332. Troost.-^. R., H (1882), p. 788; 9^ (1882), p. 1508; 95 (1882), p. 30. he Ghatelier.—C. R, 121 (1895), p. 323. {See also under Thermo- electric Pyrometer.) BertJielot. — Sganees de la soc. de physique, Paris, Feb. 1898, and Bull, du Museum, No. '6 (1898), p. 301. Callendar and Griffiths. — Proc. Eoy. Soc. London, 49 (1891), p. 56. Chappuis and Barker. — Travaux et Mem. du Bureau Int. des Poids et des Mesures, 12, 1900; Phil. Trans., 1900. Preyer and T. Meyer. — Zeits. fur Anorg. Ohem., 2 (1892), p. 1; Berl. Ber., 25 (1892), p. 622. '^ S. ToMWff.— Trans. Chem. Soc. (1891), p. 629. MaeCrae.—WieA. Ann., 55 (1895), p. 95. Callendar.— VhM. Mag. (5), 48 (1899), p. 519. (Fusion also.) VARIOUS SUBJECTS. Bolborn and Day. — On the expansion of certain metals at high temperatures. Drude's Ann., 4, 1 (1901), p. 104. Deville and Troost. — Expansion of porcelain. C. R., 57 (1863), p. 897. r. G. Bedford. — On the expansion of porcelain with rise of tempera- ture. B. A. Report, 1899. Le Chatelier. — Dilatation of ir«n, steel, copper alloys, etc. C. R., 128 (1899), p. 1444; 129, p. 331; also C. R, 107 (1888), p. 862; 108 (1896), p. 1046; 111 (1890), p. 123.— Speeifle heat of carbon. C. R., 116 (1893), p. 1051; Soc. Franc, de Phys., No. 107 (1898), 3. Barns. — Bull, of U. S. Geological Survey, No. 54, 1889. (Pyrometry.) Report on the progress of pyrometry to the Paris Congress, 1900. (This is the latest and best summary of pyrometric methods to date.) — Viscosity and temperature. Wied. Ann., BIBLIOORAPHIGAL INDEX. 223 96 (1899), p. 358; and Callendar, Nature, 49 (1899), p. 494 — Long-range temperature and pressure variables in physics. Nature, 56 (1897), p. 528. Baly and OAorJej/.— Liquid-expansion pyrometer. Berl. Ber., 27 (1894), p. 470. Dufour.—Tm in quartz-pyrometer. C. R., 180 (1900), p. 775. Berthelot. — 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 Slectrique, Paris, 1898. i?'Mej?ner.— Specific heat of gases. Wied. Beibl., 23 (1899), p. 964. Topler. — Pressure-level apparatus. Wied. Ann., 56 (1895), p. 609; 57 (1896), p. 31L Quincke. — An acoustic thermometer for high and low temperatures. Wied. Ann., 63 (1897), p. 66. K. Scheel.—VeheT Femthermometer. Verlag v. 0. Marhold, Halle, 1898. 48 pp. Eeitmann. — ^Ueber einen neuen Ttmperatur-Femmessapparat von Hartmann und Braun. E. T. Z., 19 (1898), p. 355. OTiree. — Recent work in thermometry. Nature, 58 (1898), p. 304. Limeray. — On a relation between the dilation and the fusing-points of simple metals. C. R., 131 (1900), p. 1291. GENERAL INDEX. PAOB Austen (Bobbkts), recording-pyrometer, description, 184 ; ob- servations 184-193 Baeus, fixed points 6 gas-pyrometer 40, 58, 200 pyrometry 313 thermoelectric pyrometer 97, 103 Becquerel, gas- pyrometer observations 53 thermoelectric pyrometer 92, 93 Berthelot (D.), calorimeter , 77 expansion coefficients 198 fixed points 207 optical pyrometer 66, 318 Bibliographical Index 315 Biju-Duval, calorimetric observations 80 Bolometer 138 Boltzmann, law of radiation 209 Boudouard, radiation pyrometer , 154 Callbndab, bolometer records 177 helium thermometer ] 99 notation for resistance-thermometer 204 normal scale of temperatures 33, 25 platinum thermometry 6, 8, 88-91 , 204, 207 Calorimeters, jacketed, 78 ; wooden, 81 ; precision of use 80 Chappuis, gas-pyrometer 197-200 normal scale of temperatures 18, 197 normal thermometer 36 platinum thermometer 207 ^ sulphur boiling-point 307 325 226 GENERAL INDEX. PASS. Charpy, therflioelectric recording-pyrometer 186 Clarence Works 193 Conclusion 193 Contents, table of vii Cornu, photometry 145 Coupeaux, gas-pyrometry 39 Couple (thermoelectric), advantages 127 arrangements of wires 112 chemical changes 98 choice 96 E. M. F., 118-120 ; method for measuring 99 formula for B. M. F 118, 119, 200-203 graduation, 118 ; fixed points 119, 207 heterogeneity of leads 94, 203 insulation and protection 113 junction of leads 112, 117 parasite currents 98 resistance 102 temperature measurements 126, 207 Crafts, gas-pyrometry 39, 62 normal scale of temperatures 20 Crova, radiation-pyrometer 160 Day, expansion coefficients 199 fixed points 207 gas-pyrometry 199 thermoelectric pyrometer '. 201 Dowlais, blast-furnace 192 Dufour, quartz-tin pyrometer 312 Ebullition, points of 5-7, 69-73, 207 Euchene and Duval, total heat of nickel 76 Expansion, gas, 15-17, 26, 198 ; porcelain, 39, 60, 199 ; metals . . 199 Fusion, points of, 5-8, 69, 207 ; their use 124 in gas-pyrometry 52, 57, 207 by resistance-pyrometer 90, 207 Galvanometers, thermoelectric 103 needle 110-112 GENERAL INDEX. 227 PAGE Galvanometers, movable coil 107 with microscope 108 with mirror 109 Gray, heat-radiation pyrometer. 135 Griffiths, platinum-pyrometry 6, 84, 86, 89 Heycock, resistance-pyrometer 6, 90, 207 Holborn, alteration of platinum wires 85, 204 constant-volume thermometer 199 expansion coefficients 199 fixed points 6, 56, 57, 200, 204, 207 graduation of thermo-couples 59 resistance of platinum 87 substance of thermometer-bulb 39, 199 Holman, fixed points 207 thermoelectric formulae 119, 200 iNTBODtrCTION 1 JOLLT, meldometer 137 Ktrchoff, law of 140 Langley, bolometer 138 Lauth, fusible cones 168 Le Chatelier, calorimetric pyrometer 8 high temperatures 154 nickel in calorimetry 76 optical pyrometer, 144 ; graduation of. 152 radiation-pyrometer 8, 144, 154 thermoelectric pyrometer, 8, 94, 102, 180; recording 180 Wedgwood's pyrometer 164 Lehrfeldt, normal temperature-scale 26 Lummer, laws of radiation , 209 .Mallabd, gas-pyrometer 57 Mariotte's law 10 Meldometer 137 Mesure and Nouel, radiation-pyrometer ;158 228 GENERAL INDEX. PAOI NevHiI/K, resistance-pyrometer 6, 90, 207 Pasceen, law of radiation 211 PiONCHON, total heat of nickel 77 Planck, laws of radiation 209 Pouillet, calorimetric pyrometer 75 gas-pyrometer 'w 7, 50 radiation-pyrometer 130 thermoelectric pyrometer ... 93 Preface iii Pringaheim, laws of radiation 209 Pyrometer — Galorimetric : principles of 7, 74 advantages of 7 choice of metals 75, 76 VioUe's experiments 5, 7, 55-58, 75, 131 Electrical resistance : principle of 8, 83, 204 conditions of use 91 experimental arrangement 88 researches of Siemens 83 Cfcu 7, 37, 197 experimental arrangements 60 fixed points with 5, 20, 53, 69-78, 207 indirect methods 62 substance of bulb 37-39, 199 Thermoelectric (see also Couple), principle 9, 92, 200 conditions of use 138 experimental results 127, 207 graduation 118 Le Chatelier's experiments 94 methods of measurement 99 Heat-radiation, principle 8, 129, 207 observations with 130-136 iMmiiums radiation, principle 8, 140, 143, 156, 207 conditions of use I55 Crova's form jgO Le Chatelier's photometer, 144; graduation 163 measurements with 143, 144, 149-151, 154, 209 Optical interference, of D. Berthelot 66 218 Wedgwood's 9 153 GENERAL INDEX. 229 PAGE Pyrometer — Fumble cone 9, 167 table 173 Becording 174 gas 174 resistance 176 thermoelectric 179, 192, 203 Various forma 212 Radiation (see Pyrometer), laws of /. . .137, 140, 152, 207 Randall, gas-thermometer bulb /; 38 Ranklne, variation of expansion coefficients 15 Regnault, boiling-point of mercury 90 calorlmetric pyrometer 7, 75 normal scale of temperatures 14 Rosetti, radiation-pyrometer 133 Rous, lamp of 185 SAiNTE-CLAiBE-DEViLiiK, gas-pyrometer 7, 58, 63 Scales, normal, of temperature 10, 19 thermodynamic 21 thermometric 3 . Seebeck effect , 92 Seger, fusible cones 167 table 172 Siemens, resistance-pyrometer 8, 83 Specific heats 55, 56 Stansfield, thermoelectric formula 203 thermoelectric pyrometer 202, 208 Stefan, law of radiation 137, 209 Thekmometke, Callendar's 33 gas, 11; various types 18-25 high temperature 36, 199 S6vres normal 27 Thermophone 213 Tory, platinum thermometry 204 ViOLLB, fixed points 5 calorimetric pyrometer 5, 7, 74, 131 aif-thermometer 20, 55-57 230 GENERAL INDEX. PAQE Wanhbk, law of radiation 211 Wien, alteration of platinum 85 fixed points 6, 57 graduation of thermo-couple 59 resistance of platinum 87 substance of gas-tliermometer bulb 39 Wiborgh, thermopbone 213 Wilson, heat-radiation pyrometer 135 SHORT-TITLE CATALOGUE OF THE PUBLICATIONS OF JOHN WILEY & SONS, New York. London: CHAPMAN & HALL, Limited. ARRANGED UNDER SUBJECTS. Descriptive circulars sent on application. Boolts marked with an asterisic are sold at net prices only. 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