NRLF 
 
 B 14 ESE 7bfl 
 
LIBRARY 
 
 UNIVERSITY OF CALIFORNIA. 
 
 UNIVERSITY OF CALIFORNIA 
 
 LIBRARY 
 
 OF THE 
 
 ***** NOV14j91 
 
 Accessions No. % w .V Book No.-.. 
 
LOWER DIVISION 
 
 
 i 
 
SCIENTIFIC MEMOIES 
 
 EDITED BY 
 
 J. S. AMES, PH.D. 
 
 PKOFESSOB OF PHYSICS IN JOHNS HOPKINS UNIVERSITY 
 
 XIV 
 
 THE EXPANSION OF GASES BY HEAT 
 
THE EXPANSION OF GASES 
 BY HEAT 
 
 MEMOIRS BY DALTON, GAY-LUSSAC, REGNAULT 
 AND CHAPPU1S 
 
 TRANSLATED AND EDITED BY 
 
 WYATT W. RANDALL, PH.D. 
 
 HEADMASTER OF THE MACKENZIE SCHOOL, DOBBS FERRY, N. Y. 
 
 NEW YORK :- CINCINNATI :- CHICAGO 
 
 AMEEICAN BOOK COMPANY 
 

 COPYRIGHT, 1902, BY 
 AMERICAN BOOK COMPANY. 
 
 Entered at Stationers' 1 Hall, London, 
 
 Expansion of Gases. 
 W. P. I 
 
PEEFATOEY NOTE. 
 
 IN preparing a volume to contain the classical memoirs 
 which treat of the law of the expansion of gases by heat, a 
 choice which will be satisfactory from all points of view can 
 scarcely be expected. The memoirs of Dalton, Gay-Lussac and 
 Regnault are of course given in full; were it not for the very 
 comprehensive abstract given in Regnault's first paper, the 
 memoirs of Rudberg would certainly have been included. It 
 has seemed best to the editor not to print in full any other 
 than the memoirs mentioned ; all others of sufficient import- 
 ance are referred to in the historical Introduction. An excep- 
 tion has been made, however, in the case of Chappuis's research, 
 for the proper comprehension of which a fuller abstract was 
 needed than could readily be included in the Introduction. 
 This abstract is therefore given separately. 
 
 The Bibliography contains, along with a few others closely 
 connected, a list of the memoirs printed in full or discussed in 
 the Introduction. 
 
 DOBBS FERRY, NEW YORK. 
 
GENERAL CONTENTS. 
 
 PAGE. 
 Prefatory Note ....... v 
 
 Introduction . . . . . . .3 
 
 On the Expansion of Gases by Heat. By John Dalton . 17 
 Extract f rom " A New System of Chemical Philosophy." 
 
 By John Dalton ...... 22 
 
 Biographical Sketch of Dalton ..... 22 
 
 Researches upon the Rate of Expansion of Gases and 
 
 Vapors. By L. J. Gay-Lussac . . . .25 
 
 Biographical Sketch of Gay-Lussac . . . .48 
 
 The Determination of the Rate of Expansion of Gases by 
 Heat. An extract from the " Traite de Physique " 
 of J. B. Biot ...... 51 
 
 Researches upon the Rate of Expansion of Gases. First 
 
 Memoir. By H. V. Regnault .... 63 
 
 Biographical Sketch of Regnault . . . .120 
 
 Researches upon the Rate of Expansion of Gases. Second 
 
 Memoir. By H. V. Regnault . . . - . 121 
 
 Researches upon the Gas Thermometer, and the Compari- 
 son of the Gas Thermometer with the Mercury Ther- 
 mometer. By P. Chappuis. Abstract . . .151 
 Bibliography ....... 159 
 
 Index . . . 161 
 
 vn 
 
INTRODUCTION. 
 
CONTENTS. 
 
 PAGE 
 
 Dalton . ......... 3 
 
 Gay-Lussac . . . . . . .. N . . 3 
 
 Dulong and Petit . ' . '. ... - \ 4 
 
 Flaugergues . . --. . . . -.'".' . . 5 
 Rudberg . . . , ^ . . . . 5 
 
 Magnus . s . 6 
 
 Regliault . r^ w . . . . . .... 7 
 
 Balfour Stewart . . . . . . , . . 9 
 
 Recknagel . .' .... . , . ... 9 
 
 v. Jolly . ' , . . . , . . . . 9 
 Amagat . . . . . . , . . .10 
 
 Mendeleeff and Kajander . . . . . . 11 
 
 Andrews . . . . . . . .12 
 
 Callendar and Griffiths . . . , . . . 13 
 
 Chappuis and Harker . 13 
 
 Wiebe and Bottclier . . . . . . .13 
 
 Kuenen and Randall . . . . . .14 
 
 Melander . . .14 
 
 Baly and Ramsay 15 
 
INTEODUCTION. 
 
 THE Law of the Expansion of Gases by Heat, variously 
 called the Law of Charles, Dalton, and Gay-Lussac, seems to 
 have been for the first time definitely made known to the 
 scientific world by the English chemist. As Roscoe says, 
 " This law of equal expansion of all gases for equal increments 
 of temperature has been generally known on the Continent as 
 * Gay-Lussac's ' or ' Charles's law,' but ought to be called l Dai- 
 ton's law of expansion, 'as he first announced it and gave experi- 
 mental evidence of its truth, and the claims of the Manchester 
 philosopher are generally now allowed/' (John Dalton, and the 
 Rise of Modern Chemistry, page 96.) 
 
 The experimental basis upon which Dalton founded his 
 generalization was, however, meagre and, from a modern stand- 
 point, quite inaccurate as was the case also with the evidence 
 upon the strength of which he put forth his Law of Multiple 
 Proportions and the original Atomic Hypothesis. The work 
 done upon this subject by Dalton and Gay-Lussac and es- 
 pecially by the latter, the results of which were published in 
 1802, forms an epoch in the history of the careful study of the 
 properties of gases, if for no other reason than because of the 
 recognition of the necessity for the thorough removal of water 
 vapor from the gas examined, before concurrent results could 
 be expected. 
 
 Of the investigations carried out prior to the beginning of 
 the Nineteenth Century, Gay-Lussac gives a sufficient account 
 in his first memoir. During the year 1801 Dalton read a series 
 of papers before the Manchester Society, one of which treated 
 of the rate of expansion of air and other gases and records, as 
 its author states, experiments undertaken to' test the results of 
 the research of Guyton de Morveau and Duvernois. On 
 account of its bearing upon certain theories which he held 
 upon the nature of heat, Dalton's attention was especially 
 drawn to the increase in the rate of expansion with rise of 
 
 3 
 
MEMOIRS ON 
 
 temperature, and he does not seem to have calculated an aver- 
 age coefficient of expansion on the basis of the volume of the 
 gas at the melting-point of ice, from the results of these experi- 
 ments. After the publication of Gay-Lussac's research, how- 
 ever, he apparently repeated his experiments with greater care, 
 using 32 F. as one limit of the temperature-range, and calcu- 
 lated from the results thus obtained the coefficient which in his 
 "New System" he states was the same as that announced by 
 Gay-Lussac. This matter is discussed in a footnote on page 
 72. Dalton's first paper was published before that of the 
 French savant, but in all probability not until the latter's ex- 
 perimental work had been completed. 
 
 It is singular that Gay-Lussac's later and, apparently in his 
 opinion, more accurate investigation, an account of which is 
 given in the form of an extract from Biot's Traite de Physique 
 should have been made known to the world only through 
 this means. 
 
 The results of the profound researches of Dulong and Petit 
 upon the absolute expansion of mercury and the relation be- 
 tween the mercury and gas scales of temperature, were to a 
 certain extent vitiated through their apparent acceptance of 
 the Gay-Lussac coefficient 0.00375 for the expansion of air 
 One at least of their own experiments pointed to a figure much 
 nearer that now accepted as correct, but such evidence as now 
 exists indicates the use of the higher value in their computa- 
 tions. Their method involved the use of an open air-ther- 
 mometer whose tip was sealed after it had been heated to some 
 definite temperature; after the apparatus had been allowed to 
 cool again to 0, the tip of the thermometer tube was again 
 opened under mercury and from the Amount of mercury 
 drawn in the expansion of the air at the previous high temper- 
 ature was calculatedo Practically the same method was after- 
 wards employed by Rudberg and by Regnault in their researches 
 upon the rate of expansion of gases. Assuming the coefficient 
 Oo 00375 for air and calculating on this basis the true tempera- 
 tures registered by their air thermometers, Dulong and Petit 
 naturally found greater deviation from the air standard on the 
 part of mercury than the more accurate work of Regnault and 
 others has since proved to exist. Since the coefficient of ex- 
 
 4 
 
EXPANSION OF GASES 
 
 pansion of mercury found by them has been shown by more 
 recent investigations to be very nearly exact, it remains but to 
 substitute the correct value for the coefficient of expansion of 
 air to determine, with only slight error, the actual deviation of 
 the mercury scale from the air scale of temperature. 
 
 In Gehler's Physikalisches Worterbuch (1825) an account is 
 given of two researches upon the rate of expansion of air by 
 H. Flaugergues, published in the Journal de Pharmacie. 
 Using a glass flask similar to that employed by Gay-Lussac in 
 his earlier experiments, he found 0.371168 for the amount of 
 the expansion of unit volume of air between and 80 R If 
 allowance must be made for the expansion of the flask, this 
 fraction becomes 0.375671 nearly the same as Gay-Lussac's. 
 It is not clear from the context that Flaugergues took the 
 expansion of the flask into account ; nevertheless it is likely, 
 and the coefficient first given, 0.00371, is probably his corrected 
 resulto The fact of the expansion of the containing vessel was 
 at that time well known and generally allowed for ; besides, in 
 the experiments described in the second, paper the author 
 made use of a method intended to eliminate this factor : the 
 gas was contained in a cylindrical glass vessel in which was a 
 smaller leaden cylinder ; the greater rate of expansion of the 
 lead was to bring about a decrease of the vessel's capacity for 
 gas exactly compensating for the increase in the size of the 
 glass envelope. These experiments led to the figure 0.37174 
 for the amount of the expansion between and 80 R. 
 practically identical with the former result. An experiment 
 with moist air yielded as a result 0.411. 
 
 The determinations of Flaugergues seem to have attracted 
 little attention, and, although they had pointed out the possi- 
 bility of error in Gay-Lussac's coefficient, it was not until the 
 publication of the very noteworthy memoirs of Rudberg that 
 the matter received due consideration. 
 
 In the course of an investigation which had for its object the 
 accurate determination of the melting points of the metals 
 lead, tin and antimony on the scale of the air thermometer, 
 Rudberg had found that, assuming Gay-Lussac's coefficient 
 0,00375 to be correct, he was led to conclude that the coefficient 
 of expansion of glass was far greater at high temperatures than 
 
 5 
 
ME MO IBS ON 
 
 its behavior at ordinary temperatures would appear to promise. 
 He accordingly undertook the re-determination of the air 
 coefficient, employing, first, a method in which both volume 
 and pressure varied, and, second, one in which the volume 
 remained constant. The original memoirs are not given in 
 the form of translation in this volume, as a sufficient abstract 
 of them is given by Regnault in his- first paper. 
 
 It will be well, in passing, to call attention to the fact that the 
 first method of experiment employed by Rudberg was that 
 which had been used previously by Dulong and Petit, but that 
 the second seems to have been original with him ; except for 
 comparatively slight modifications intended to secure greater 
 accuracy, the constant-volume air thermometer of to-day is the 
 invention of Rudberg. 
 
 Both methods of determination led to the same result : Gay- 
 Lussac's coefficient is too high by about one part in thirty-seven ; 
 the figure adopted by Rudberg as the probable coefficient of 
 expansion of air is "between 0.00364 and 0.00365." It had 
 been his intention to investigate other gases as well, but his 
 death occurred shortly after the publication of the results 
 obtained for air. 
 
 The great importance of the question involved was generally 
 recognized and, consequently, within about four years the 
 results of two careful, quite independent, investigations, one 
 by Magnus in Berlin, the other by Regnault in Paris, made 
 their appearance. While neither of them was led to a figure 
 for the air coefficient quite so low as that adopted by Rudberg, 
 both were able to support the latter's contention that the 
 coefficient found by Gay-Lussac was far too high. It is interest- 
 ing to note, however, that just as the more accurate work of 
 Magnus and Regnault showed that Rudberg's coefficient was too 
 low, exactly the same fate has befallen the coefficient adopted 
 by Magnus and Regnault, through the investigations carried 
 out since 1860. 
 
 Magnus as did also Regnault endeavored to repeat the 
 later experiments of Gay-Lussac with air at constant pressure, 
 but found it impossible to secure uniform results, evidently 
 because the short mercury piston failed to close completely the 
 bore of the thermometer tube : air leaked in or out according 
 
 6 
 
EXPANSION OF OASES 
 
 to the direction of movement of the mercury index and the 
 relative tension within and without the tube. Turning to 
 Rudberg's second method : that by which the increase of 
 pressure within a gas reservoir of constant volume was measured 
 instead of the increase in the volume of a gas kept at constant 
 pressure : Magnus obtained eight values for a ranging from 
 0.00365032 to 0.00367899 with a mean of 0.00366508 at a 
 barometric pressure of 28 inches ; at 760 mm. pressure this 
 mean value becomes 0.0036678. At 28 inches pressure the 
 mean coefficient found for hydrogen was 0.00365659 ; for car- 
 bon dioxide, 0.00369087 ; for sulphur dioxide, 0.00385618, 
 While the mean value for air found by Magnus, after recalcula- 
 tion for a pressure of 760 mm., is nearer than is the mean 
 value found by Regnault by his four different methods, to the 
 coefficient for constant volume now accepted, this fact cannot 
 be interpreted as a proof of greater accuracy of experimental 
 work on the part of the German physicist. Regnault's lowest 
 result was 0.0036549, and highest 0.0036747 a range of 
 0.0000198 in fifty determinations carried out by four distinct 
 methods ; for any one method the range amounted to but two 
 thirds of this amount, at the most. On the other hand, 
 Magnus's results, all by one method and only eight in number, 
 ranged 0.00002867. For hydrogen the range from highest to 
 lowest was 0.0000029 in four determinations ; for carbon dioxide, 
 0.00002228 in four ; for sulphur dioxide, 0.00006552 in three 
 determinations. 
 
 Magnus suggests as a possible explanation of the difference 
 between the results of Gay-Lussac and those of Rudberg and 
 himself, among other things, the fact that the former's gas 
 reservoir was actually in the boiling water of the bath instead 
 of in its vapor. 
 
 Regnault's two memoirs on the expansion of gases are given 
 in full in the form of a translation. It is to be noted that he 
 employed with success five different forms of apparatus to 
 determine this expansion between and 100 : in the first of 
 these both volume and pressure varied to a considerable degree ; 
 in the second the volume remained more nearly constant ; in the 
 third and fourth the volume changed only to the extent of the 
 expansion of the glass envelope ; while in the fifth the increase 
 
 7 
 
MEMOIRS ON 
 
 of volume was directly determined under constant pressure. 
 The last mentioned method established the fact that for most 
 gases the coefficient of expansion at constant pressure is slightly 
 greater than that at constant volume, because such gases do 
 not exactly conform to Boyle's Law, but contract more rapidly 
 in proportion than the pressure upon them increases. Thus 
 the mean value found for air at constant volume is stated by 
 Regnault to be 0.003665, and that for constant pressure, 
 0.0036706, at about atmospheric pressure. The latter coeffi- 
 cient increases as the pressure is increased : at about 3 atmos- 
 pheres it is between 0.00369 and 0.00370. 
 
 Both Magnus and Regnault then proceeded independently to 
 re-determine the variation between the mercury scale and the 
 air scale of temperature. Since the data showing the dimen- 
 sions of the apparatus of Dulong and Petit were unknown, it 
 was impossible with certainty to re-calculate their results with 
 the aid of a more nearly correct coefficient of expansion for air. 
 Gay-Lnssac had declared that air and mercury expand pro- 
 portionally even at comparatively high temperatures ; Dulong 
 and Petit found in their research that soon after passing 100 
 mercury began to expand more rapidly, and that at about 300 
 the temperature by the mercury scale was over 7 higher than 
 that calculated from the readings of their air thermometer. 
 
 Here, again, the superiority of the experimental work of 
 Regnault cannot be questioned. It established the fact that 
 the air thermometers and the mercury thermometers agree up to 
 about 250 ; above this point mercury expands more rapidly in 
 proportion than air, and at 350 (by the air thermometer) the 
 mercury thermometer stands about 3 higher. 
 
 Magnus's work, on the other hand, led to the practical con- 
 firmation of the results of Dulong and Petit. As Magnus had 
 used the coefficient 0.003665 (at 28 inches ; 0.0036678 at 760 
 mm.) in calculating his air thermometer temperatures, he was 
 led to believe that Dulong and Petit had not after all made use 
 of Gay-Lussac's coefficient, but that, having in a single inde- 
 pendent determination as was known found the coefficient 
 0.00365, they had employed the latter instead. This sup- 
 position Regnault, in criticizing Magnus's results, considered 
 extremely unlikely, on the ground that a study of Dulong and 
 
 8 
 
EXPANSION OF OASES 
 
 Petit's results does not seem at all to confirm it, and that the 
 latter would hardly have depended upon a single determination 
 of so important a factor, especially when so at variance with 
 the generally accepted figure of Gay-Lussac. Into the 
 criticisms passed upon one-another's apparatus there is no need 
 here to go. 
 
 An investigation of the behavior of gas thermometers at 
 about 88 led Eegnault to the conclusion that the coefficients 
 of expansion for air and hydrogen preserve closely the ratio 
 shown at higher temperatures. 
 
 In his comparison of the various gas thermometers in the 
 Memoires of the Academy of Sciences, Regnault speaks of using 
 a coefficient for hydrogen smaller than he records in any of his 
 experiments. Lord Kelvin has called attention to the fact that 
 this statement is probably in error (See Encyclopedia Britan- 
 nica, article "Heat"). 
 
 Mention may be made here, finally, of the study by Regnault 
 of the coefficient of expansion of gases under high pressures, 
 the results of which are contained in a later volume of the 
 Memoires. 
 
 The accuracy of the results of Regnault for air at constant 
 volume was put to the test by Recknagel and, still more rigor- 
 ously, by Balfour Stewart ; the results of the former confirmed 
 those of Magnus, so far as the value of the coefficient is con- 
 cerned, Recknagel's mean value being 0.0036681. Stewart, like 
 Recknagel, used the method employed successfully by Rudberg, 
 Magnus and Regnault to find the coefficient of expansion from 
 the rise of tension in a gas kept at constant volume while its 
 temperature rises, but, using even greater care than did any of 
 his predecessors to secure pure dry air for his apparatus, and 
 employing every known refinement in the measurement of the 
 pressure changes, he obtained the figure 0.0036728 as the 
 average of four results, the highest of which was 0.0036739 and 
 the lowest, 0.0036716. 
 
 The results recorded in the memoir of v. Jolly, although 
 scarcely to be compared as regards accuracy with those of 
 Stewart, are interesting because of the author's success in 
 simplifying the constant-volume gas thermometer. The differ- 
 ences between his highest and lowest results were, how- 
 B 9 
 
MEMOIRS ON 
 
 ever, not so great as those between the corresponding figures 
 in the several series of Regnaolt's determinations. He was also 
 successful in determining the coefficient of expansion of oxygen, 
 which Regnault had failed to do. For air, v. Jolly found in 20 
 experiments: highest, 0.0036724; lowest, 0.003665; mean, 
 0.00366957. For oxygen (18 experiments) the highest was 
 0.003680 ; lowest, 0.0036683 ; mean, 0.0036743. For hydrogen, 
 the highest of 4 results was 0.0036600 ; lowest, 0.0036530 ; 
 mean, 0.0036562. For nitrogen, the highest of 4 results was 
 0.0036717 ; lowest, 0.0036655 ; mean, 0.01/36677. For carbon 
 dioxide, the highest of 17 results was 0.0037144 ; lowest, 
 0.0036962 ; mean, 0.0037060. 
 
 Of the extensive and important researches of Amagat one 
 memoir and part of another have appeared in the form of a 
 translation in an earlier volume of this series " The Laws of 
 Gases : Memoirs by Boyle and Amagat." Earlier than either 
 of these is a study (1873) of the variation of the coefficient of 
 expansion of gases with rise of temperature ; a constant-vol- 
 ume method based upon that of Rudberg was employed. 
 Assuming that for air the mean value of a == 0.00367 between 
 and 100, he finds the mean values of a for sulphur dioxide 
 and carbon dioxide steadily decrease as the temperature rises. 
 Thus, for the former gas it is 0.003904 between 10 and 60, 
 but 0.003798 between 10 and 250; between and 10 it is 
 0.00413, at 25 0.00394, at 100 0.003757, at 250 0.003685. 
 For carbon dioxide the mean value of a between and 50, 
 is 0.003714; between and 250 , 0.0037028; at it is 0.003724; 
 at 50, 0.003704; at 100, 0.003695; at 250, 0.003682. 
 
 From the memoir of 1881, the following may be quoted with 
 regard to the behavior of gases under high pressures: 
 
 "1. The coefficient of expansion of gases {referred to unit 
 volume) increases with the pressure up to a maximum value, 
 beyond which it decreases indefinitely. 
 
 " 2. The maximum occurs at a pressure for which the pro- 
 duct^ is a minimum; consequently at this point the gas acci- 
 dentally obeys Marietta's law. 
 
 " 3. For continually rising temperatures this maximum be- 
 comes less and less distinct and, finally, disappears." 
 
 Hydrogen even at very low pressures seems already to have 
 
 10 
 
EXPANSION OF GASES 
 
 passed the point where ^ is a minimum; hence its coefficient 
 constantly decreases as pressure rises and as temperature rises. 
 The pressures employed in these experiments ranged from 40 
 to 320 metres of mercury. 
 
 In a later memoir (1893) are recorded results obtained 
 through a still greater range of pressures. Amagat says, " An 
 inspection of Table 21 shows that at the outset the coefficient 
 of expansion increases with the pressure, as Regnault had 
 already found for pressures of a few atmospheres ; it then 
 passes through a maximum which occurs at a pressure rising 
 regularly with the temperature. During my first researches 
 on this subject these maxima seemed to coincide with those 
 pressures for which the product pv is a mimimum; but the 
 more extended data of the present memoir show this law to be 
 only approximate." With rise of pressure from 1000 to 3000 
 atmospheres, the coefficient of expansion of oxygen between 
 and 16 steadily decreased from 0.00236 to 0.00134, that of 
 hydrogen from 0.00200 to 0.00128, that of nitrogen from 
 0.00193 to 0.00098, and that of air from 0.00206 to 0.00110. 
 Another series of experiments showed that with rise of pressure 
 from 200 to 1000 atmospheres a similar fall in the value of the 
 coefficient was to be noted. The coefficient in the case of car- 
 bon dioxide rises to a maximum and decreases; this maximum 
 occurs at higher and higher pressures as the temperature rises: 
 thus, at 137 198, a is 0.00369 (of the volume at 137 con- 
 sidered as unity) when the pressure is 75 atmospheres; 0.00798 
 (maximum value) at 200 atmospheres, 0.00386 at 500, and 
 0.00223 at 900 atmospheres. The coefficient of carbon dioxide 
 for constant pressure rises at first with the temperature, passes 
 a maximum, and then decreases as temperature rises; as the 
 pressure is higher, the maximum occurs at higher and higher 
 temperatures. 
 
 The elaborate investigations of Mendeleeff upon the proper- 
 ties of gases are to a large extent a terra ignota for those who 
 cannot read Russian ; only a few papers, usually meagre ab- 
 stracts, contained in journals published in Western Europe, are 
 available as sources of information. In papers published in 
 conjunction with Kajander, he discussed the disadvantages of 
 Regnault's constant-pressure method, among others that only 
 
 11 
 
MEMOIRS ON 
 
 about two thirds of the gas contained in the apparatus was at 
 the temperature of the water vapor. In fact, in his Princi- 
 ples of Chemistry (2nd Edition, Volume 1, page 133, note), 
 he goes so far as to state " Regnault, however, did not directly 
 determine the change of volume between and 100, but 
 measured the variation of tension with the change of tempera- 
 ture; but since gases do not entirely follow Mariotte's law, the 
 change of volume cannot be directly judged by the variation 
 of tension." Nine results obtained with an apparatus in which 
 the entire volume of gas was surrounded with water vapor, and 
 various devices were employed to increase the accuracy of the 
 readings, ranged from 0.0036814 to 0.0036876, with a mean of 
 0.0036843. This is the coefficient of expansion of air at a con- 
 stant pressure of about 760 mm.; the probable error of the 
 mean value is estimated by Mendeleeff to be 0.0000005. 
 
 In his Principles of Chemistry Mendeleeff gives the results 
 obtained at constant volume: for air, 0.00368; for hydrogen, 
 0.00367; for carbon dioxide, 0.00373; for hydrobromic acid 
 gas, 0.00386. At 3 atmospheres pressure a becomes 0.00371 
 in the case of air. The coefficient of expansion of carbon 
 dioxide rises with pressure as follows : at 1 atmosphere, 0.00373; 
 at 3, 0.00389; at 8 atmospheres, 0.00413. In the case of hydro- 
 gen which is, on the other hand, less compressible than Boyle's 
 Law would lead one to expect, the rise of the coefficient with 
 increase of pressure is slower: at one atmosphere it is 0.00367; 
 at eight atmospheres, 0.00369. 
 
 In one paper Mendeleeff recalculates the results of Magnus, 
 Regnault and v. Jolly for air at constant volume, reducing the 
 barometric readings to 45 latitude. He gives the following 
 table: 
 
 Determinations As given by author Corrected value. 
 
 Magnus 8 0.0036651 0.0036700 
 
 Regnault 15 0.003665 0.0036694 
 
 v. Jolly 20 0.0036696 0.0036702 
 
 Mean, 0.003670 
 
 The coefficient for constant pressure, as found by himself 
 with Kajander, is recalculated in the same way and given as 
 0.003681. 
 
 The investigations of Andrews upon the critical state, 
 
 12 
 
EXPANSION OF GASES 
 
 among other points, led to a study of the coefficient of expan- 
 sion of carbon dioxide at higher pressures. He gives the 
 following figures for a (constant pressure) atO 7.5 : 
 
 ftaSr^I 12 16 ' 25 20 ' 01 24 ' 8 27 ' 7 3L1 34 ' 5 
 Coefficient 0.00462 0.00520 0.00607 0.00700 0.00782 0.00895 0.01097. 
 
 The value of a (64 -100) increases with increasing pressure 
 up to 0.01822 at 145.5 atmospheres; then decreases: at 223 
 atmospheres, a = 0.0084. 
 
 The coefficient for constant volume rises from 0.003526 at 
 21-24 atmospheres to 0.007018 at 94-118 atmospheres. 
 
 Several researches conducted during the past fifteen years 
 have shown extraordinary improvement in the accuracy of 
 measurement of pressure changes in gas thermometers. The 
 researches of Callendar upon the platinum thermometer and its 
 standardization by means of the gas thermometer, have led to 
 the improvement of the latter as an instrument for exact 
 determinations. The work of Cbappuis is so striking an 
 example of the kind of accuracy referred to, that a much more 
 detailed abstract of his memoir is given in the body of the 
 book (page 153). The coefficients for hydrogen as found by 
 him are : constant volume, 0.0036624 ; constant pressure, 
 0.0036600. If these are reduced to their limitary values which 
 refer to zero pressure, they become 0.0036624 and 0.0036625 
 respectively, giving as "absolute zero "on the centigrade scale 
 -273.04. The mean coefficient of expansion found by him for 
 nitrogen, at constant volume, between and 100 is 
 0.00367466. The figure found for air by Callendar and Grif- 
 fiths is almost identical, 0.0036749. The latter was, however, 
 the result of but a single determination. Wiebe and Bottcher 
 found an average value of 0.0036706 for air, in a series of figures 
 ranging from 0.0036694 to 0.0036713. Finally, Harker and 
 Chappuis, in a recent memoir, find as the coefficient of expan- 
 sion of nitrogen at constant volume (in glass) the figure 
 0.00367180 for an initial pressure of 793.5 mm. of mercury, and 
 0.0036683 for an initial pressure of 530.8 mm. of mercury. In 
 the limit, then, at zero pressure, it would be 0.0036613. The 
 limiting value for the coefficient at constant pressure is 
 0.0036612. These results indicate the limit of accuracy 
 attained up to this time. 
 
 13 
 
MEMOIRS ON 
 
 In 1895 Kuenen and Randall examined the rate of expansion 
 of argon and helium through a considerable range of tem- 
 perature ; the fact that the coefficient remained almost constant 
 showed the absence of dissociation in the gases examined and 
 was taken as proof of their simple molecular condition. 
 
 Before closing, reference should be made to work done in 
 tho study of the behavior of gases at very low pressures. The 
 results of the research of Melander are summarized in the 
 following table, where p = initial pressure, p = final pressure, 
 a = coefficient of expansion at the pressure p' \ the probable 
 error as calculated by Melander, is given for the first and last 
 values of a only, these being the limiting values. 
 
 P 
 
 752 
 
 376 
 
 260 
 
 170 
 
 100 
 78 
 51.8 
 29.1 
 13.2 
 6.6 
 
 749 
 
 254 
 
 101 
 
 75 
 
 18.6 
 5.8 
 
 749 
 
 347 
 
 267 
 
 169.5 
 
 101.5 
 55.8 
 18.1 
 
 764.5 
 351.7 
 191.0 
 111.7 
 
 48.4 
 
 20.1 
 
 9.3 
 
 1027.7 
 
 513.7 
 
 355.2 
 
 232.2 
 
 136.6 
 
 106.6 
 
 70.8 
 
 38.8 
 
 18.1 
 
 9.1 
 
 I AIR. 
 a 
 
 0.0036660 
 6624 
 6606 
 6594 
 6630 
 6657 
 6717 
 6853 
 7172 
 7627 
 
 II AIR. 
 
 1023.4 
 
 346.9 
 
 138.0 
 
 102.5 
 
 25.5 
 
 7.98 
 
 0.0036642 
 6580 
 6634 
 6645 
 6895 
 7666 
 
 III CARBON DIOXIDE. 
 
 102S.1 
 
 474.9 
 
 365.2 
 
 231.7 
 
 138.7 
 
 76.2 
 
 24.7 
 
 0.0037264 
 6856 
 6803 
 6701 
 6657 
 6641 
 6753 
 
 IV HYDROGEN. 
 
 1043.6 
 
 480.1 
 
 260.8 
 
 152.5 
 
 66.2 
 
 27.4 
 
 12.8 
 
 0.0036504 
 6518 
 6547 
 6548 
 6595 
 6721 
 7002 
 
 14 
 
 Error 
 0.0000005 
 
 0.0000021 
 0.0000004 
 
 0.0000021 
 0.0000005 
 
 0.0000015 
 0.0000002 
 
 0.0000022 
 
EXPANSION OF GASES 
 
 It will be noted that with decrease of pressure the value of a 
 falls until a minimum is reached and then rises again ; with 
 hydrogen, on the one hand, the minimum seems to have been 
 reached at about atmospheric pressure ; with air the minimum 
 occurs at about 300 mm. pressure, and with carbon dioxide at 
 about 100 mm. 
 
 The accuracy of the results obtained by other experimenters 
 at very low pressures, has been challenged by Baly and Earn- 
 say, who point out the difficulty of the removal of all gas from 
 a glass vessel and the likelihood of the presence in the gas 
 examined of carbon dioxide and water vapor given off from 
 the walls of the vessel after the pressure has been lowered. The 
 shrinkage of the vessel under atmospheric pressure after the 
 removal of most of the gas contained in it, is another source of 
 serious error. Of course these difficulties become important 
 only at very low pressures. The following table contains the 
 figures found for the coefficients of expansion of hydrogen, 
 oxygen and nitrogen at pressures below 5.5 mm. : 
 
 I Hydrogen. 
 
 Pressure in mm. 4.7 3.47 0.25 0.096 0.077 
 
 -f 277T.S ST^.T? 1T7S 5^7 THlW 
 
 (0.003656 0.003653 0.003623 0.003366 0.003327 
 
 II Oxygen. 
 
 Pressure in mm. 5.1 5.3 4.0 2.5 1.4 0.083 0.07 
 
 4 ? ^T *^tf *&* ? ^ T SsV.T T^TT ?l? ??V.3" 
 (0.0038310.0038460.003817 0.0039840.003998 0.004292 0.004098 0.004161 
 
 III Nitrogen. 
 
 Pressure in mm. 5.3 4.97 3.0 1.1 0.8 
 
 Coefficient 
 
 0.003290 0.003238 0003315 0.003290 0.003021 
 Pressure in mm. 0.6 0.6 0.6 0.6 
 
 *ks *&, * 377 dfTT THfT *$? 37T T^S 
 
 0.0028170.002911 0.0026530.003096 0.0033220.003058 0.0026950.002915 
 
 Mean of eight results at 0.6 mm. = 7 J. 5T * [=0.002919]. 
 
 Baly and Ramsay give their results in common fractions ; the 
 
 corresponding decimal fractions have been introduced for the 
 
 15 
 
EXPANSION OF GASES 
 
 sake of comparison with the results of others. The authors 
 sum up their results as follows : 
 
 "1. The coefficient of expansion of hydrogen with tem- 
 perature decreases as pressure is lowered. It is normal down 
 to a pressure of 0.1 mm. 
 
 " 2. The coefficient of expansion of oxygen is greater than the 
 normal one, being ^-^ instead of ^3 ; it increases with decrease 
 of pressure to ^^ at 1.4 mm. ; at 0.7 mm. of pressure it is 
 erratic ; but at lower pressures it again becomes more constant, 
 still showing, however, a tendency to increase as the pressure is 
 decreased. 
 
 " 3. With nitrogen the coefficient of expansion is lower than 
 the normal (^&?) at pressures between 5 and 1 mm. ; at lower 
 pressures, like that of hydrogen, its coefficient of expansion 
 decreases ; that is, the gas becomes more elastic. 
 
 " 4. So far as it was possible to experiment with carbon 
 dioxide, its behavior appears to resemble that of hydrogen and 
 nitrogen, but owing to the tendency which it has to condense 
 and cling to the gauge, trustworthy measurements were im- 
 possible to. attain. These results confirm those of Mendeleeff 1 
 and Siljestrom, 2 although they are deduced from thermal ex- 
 pansion, while theirs were deduced from the compressibility 
 of the gas. And Bohr's results 3 as regards the abnormality 
 of oxygen were also confirmed, although likewise by a different 
 method." 
 
 1 Annales de Chimie et de Physique, [5] 9, 111-116 (1876). 
 
 2 Bihang till K. Svenska Vet. Akad. Handlingar., 2, 1 (1873) ; Pog- 
 gendorff's Annalen, 151, 462-482, 573-603 (1874). 
 
 3 Wiedei luann's Annalen, 27, 459-479 (1886). 
 
 16 
 
EXPERIMENTAL ESSAYS 
 
 On the Constitution of Mixed Gases; On the Force of Steam 
 or Vapor from Water and other liquids in different tempera- 
 tures, both in a Torricellian Vacuum and in Air; On Evapora- 
 tion; and on the Expansion of Gases by Heat 
 
 BY JOHN DALTOIT 
 
 From the Memoirs of the Literary and Philosophical Society 
 
 of Manchester , volume 5, part 2, pages 595-602 (1802) 
 Translated into German: Gilbert's Annalen, volume 12, pages 
 310-318 (1802) 
 
 17 
 
CONTENTS. 
 
 PAGE 
 
 Object . i - . . . . .19 
 
 Necessity of drying gases experimented with . . 19 
 
 Apparatus used; manipulation . . . 19, 20 
 
 Results . . . . . 20, 21 
 
 Comparative expansion in lower and upper parts of thermo- 
 meter scale . . . . . .21 
 
 Experiments with gases other than air . . .21 
 
 Conclusions . . . . . . .21 
 
 Biographical Sketch ... . . . .22 
 
 18 
 
ON THE EXPANSION OF GASES BY HEAT. 
 
 BY JOHN DALTON. 
 
 THE principal occasion of this essay is another tm the same 
 subject by Messrs, de Morveau and du Vernois in the first vol- 
 ume of the Annales de Chimie. It appearing to them that the 
 results of the experiments of De Luc, Col. Hoi, de Saussure, 
 Priestley, Vandermonde, Berthollet and Monge did not suffi- 
 ciently accord with one another; and that it would be of 
 importance to determine not only the whole expansion of each 
 gas from two distant points, such as the freezing and boiling, 
 but likewise whether that expansion be uniform in every part 
 of the scale, they instituted a series of experiments expressly 
 for those purposes. The result of which was that betwixt the 
 temperatures of 32 and 212, the whole expansion of one gas 
 differs much from that of another, it being in one case about 
 -^ of the original, and in others more than 12 times that expan- 
 sion; and that the expansion is much more for a given number 
 of degrees in the higher than in the lower part of the scale. 
 These conclusions were so extremely discordant with and even 
 contradictory to those of others, that I could not but suspect 
 some great fallacy in them, and found it in reality to be the 
 fact: I have no doubt it arose from the want of due care to 
 keep the apparatus and materials free from moisture. 
 
 My method of experimenting on this subject is simple, and 
 therefore less liable to error. A straight manometer tube, such 
 as has been mentioned, is duly divided into equal portions of 
 capacity; it is then dried by a wire and thread, and the open 
 end inserted through a cork into a phial containing sulphuric 
 acid, in order that the aqueous vapour may be drawn out of 
 the tube; this is essential if we operate in temperatures 
 lower than that of the atmosphere, otherwise not. For want 
 of this attention, Col. Roi, in his valuable paper in the Phil. 
 Trans, vol. 67, has been led into some erroneous conclusions. 
 A small column of dry mercury is then let down to a proper 
 
 19 
 
MEMOIRS ON 
 
 point in the manometer, and it is ready for experiment with 
 common air. 
 
 It requires some address to fill the manometer with any other 
 gas. I succeeded best as follows: filled the tube with dry 
 mercury; then pushed down a wire and thread, so that when 
 the wire was got to the end of the tube, a thick covering of 
 thread just entered the open end, and held the mercury like a 
 cork, so that ihe tube could be inverted without losing the con- 
 tents; then having a glass funnel with a perforated cork over 
 the water apparatus, containing the gas, I slipped the mano- 
 meter through the hole in the cork, and putting my hand into 
 the water under the funnel, drew the wire out of the mano- 
 meter, and with it the mercury; upon which the gas entered 
 the manometer. For carbonic acid gas, I opened the sealed 
 end of the manometer, drew it out to a capillary bore, and 
 forced a stream of the gas through the tube; then putting my 
 finger on the other end, sealed it again by a blowpipe, and let 
 down a small column of mercury to the proper point. 
 
 When the manometer was to be exposed to a heat of 212, I 
 used a Florence flask with a long glass tube corked into it, in 
 such sort that as much of the manometer as was necessary to 
 be exposed to the temperature might be in the tube; then 
 water at the bottom of the flask was made to boil violently, so 
 that a constant stream of vapour issued out of the top of the 
 glass tube, which was found to raise the thermometer to 212. 
 Small specks of white paint were put upon the divisions of the 
 manometer together with numbers which were discernible 
 through the containing tube. For lower temperatures a deep 
 tin vessel containing hot water was used in which the mano- 
 meter was immersed, the water being well agitated previously 
 to each observation. 
 
 From a great many experiments made in this way on com- 
 mon air, and likewise upon hydrogenous gas, oxygenous and 
 nitrous gases, and carbonic acid gas, I can assert that the con- 
 clusions of DeLuc, Roi, Saussure, Berthollet, etc., are nearly 
 accurate throughout, and that those of de Morveau and du Ver- 
 nois are extremely inaccurate in the higher temperatures. 
 
 I have repeatedly found that 1000 parts of common air of 
 the temperature 55 and common pressure, expand to 1321 
 
 20 
 
EXPANSION OF GASES 
 
 parts in the manometer; to which adding 4 parts for the cor- 
 responding expansion of glass, we have 325 parts increase upon 
 1000 from 55 to 212; or for 157 of the thermometric scale. 
 As for the expansion in the intermediate degrees, which Col. 
 Roi's experiments show to be a slowly diminishing one above 
 the temperature of 57, but which de Morveau's on the con- 
 trary show to be a rapidly increasing one in the higher part of 
 the scale; I am obliged to allow that Col. Koi is right, though 
 it makes in some degree against an hypothesis I have formed 
 relative to the subject; he has certainly however made the 
 diminution too great from 72 downwards, owing to his not 
 perceiving that he actually destroyed a portion of the elastic 
 fluid he was operating upon (aqueous vapour) in reducing its 
 temperature so low; if his air had been previously dried by sul- 
 phuric acid, etc., he would not have found so remarkable 
 diminution below 72 . My experiments give for 77^ above 55 , 
 167 parts; for the next 77 only 158 parts: and the expansion 
 in every part of the scale seems to be a gradually diminishing 
 one in ascending. 
 
 The results of several experiments made upon hydrogenous 
 gas, oxygenous gas, carbonic acid gas and nitrous gas, which 
 were all the kinds I tried, agreed with those on common air 
 not only in total expansion, but in the gradual diminution of 
 it in ascending : the small differences observed never exceeded 
 6 or 8 parts on the whole 325 ; and differences to this amount 
 will take place in common air when not freed from aqueous 
 vapour which was the situation of all my factitious gases. 
 
 Upon the whole therefore I see no sufficient reason why we 
 may not conclude, that all elastic fluids under the samepressure 
 expand equally by heat and that for any given expansion of 
 mercury, the corresponding expansion of air is proportionally 
 something less, thehigher the temperature. 
 
 This remarkable fact that all elastic fluids expand the same 
 quantity in the same circumstances, plainly shows that the ex- 
 pansion in solid and liquid bodies seems to depend upon an ad- 
 justment of the two opposite forces of heat and chemical af- 
 finity, the one a constant force in the same temperature, the 
 other a variable one, according to the nature of the body ; 
 hence the unequal expansion of such bodies. It seems there- 
 
 21 
 
MEMOIKS ON 
 
 fore that general laws respecting the absolute quantity and the 
 nature of heat, are more likely to be derived from elastic fluids 
 than from other substances. 1 
 
 Dalton, in his New System of Chemical Philosophy (London: 
 1808), page 19, in discussing a proposed new method of denot- 
 ing temperature, says in reference to the expansion of gases: 
 "The volume at 32 is taken 1000, and at 212, 1376 accord- 
 to Gay-Lussac's and my own experiments. As for the expan- 
 sion at intermediate degrees, Gen. Roy makes the temperature 
 at midway of total expansion, 116 old scale ; from the re- 
 sults of my former experiments (Manch. Mem. Vol. 5, Part 2, 
 page 599), the temperature may be estimated at 119; but I 
 had not then an opportunity of having air at 32. By my 
 more recent experiments I am convinced that dry air at 32 
 will expand the same quantity from that to 117 or 118 of 
 common scale, as from the last term to 212. According to 
 the theory in the above Table it appears, that air of 117 will 
 be 1188, or have acquired one half its total expansion. Now 
 if the theory accord so well with experiment in the middle of 
 the interval, we cannot expect it to do otherwise in the inter- 
 mediate points. " 
 
 BIOGRAPHICAL SKETCH. 
 
 John Dalton was born in Cumberland, England, in the year 
 1766. He was to a large extent self-taught and, when grown, 
 was able to support himself by teaching school while, through 
 the kindness of a friend, who helped him by lending him books 
 on scientific subjects, he studied hard to acquire a knowledge 
 of natural philosophy. His papers on meteorological subjects 
 drew attention to him and in 1793 he was appointed to the pro- 
 fessorship of mathematics and natural philosophy in the Man- 
 chester New College. Simultaneous observations made in Cum- 
 
 1 Note by Translator: The paper concludes with an exposition of 
 Dalton's theory that the absolute temperature increased at the same rate 
 as the cube root of the volume in the case of gases, by which he finds the 
 temperature of absolute cold to be 1515 below F. 
 
 22 
 
EXPANSION OF GASES 
 
 berland and at Manchester enabled him to calculate the height 
 of the aurora from the earth's surface. The fact that water 
 vapor exists mixed, and not combined, in the air was announced 
 by him at this time. In 1794 he called attention to the ex- 
 istence of color blindness or " Daltonism/' as it was sometimes 
 called, having discovered that it was a feature of his own vision. 
 Continuing his meteorological studies, he was led to giving a 
 definition of the " dew-point/' In 1800 he noted the rise of 
 temperature which takes place in gases when compressed. Of 
 the four important papers read before the Manchester Society 
 in 1801, the fourth is the one quoted in full. In the first he 
 brings out " Dalton's law of mixed gases," assuming that gas 
 particles are elastic only towards particles of the same kind. 
 In the second paper, " On the force of steam/' he describes 
 the dew-point hygrometer and predicts the liquif action of gases 
 by cold and pressure. In the third paper he shows that evap- 
 oration is proportional to the temperature, whether in air or in 
 vaouo. That four such contributions to science should have been 
 presented at one time is striking proof of the extraordinary 
 powers of their author. 
 
 The data upon which the Law of Multiple Proportions is 
 based were next brought forward and, soon after, in 1803-5, the 
 Atomic Hypothesis and the announcement of the atomic 
 weights of some of the elements. Following the promulgation 
 of his views in Thomson's System of Chemistry (1807), Dalton 
 published in 1808 his New System of Chemistry. In this he an- 
 ticipated in a way Dulong and Petit/s Law, for he seemed to as- 
 sume for the atoms of all elements equal capacity for heat. 
 
 In 1825, on the establishment of the Royal Society Prize, it 
 was first bestowed upon Dalton in recognition of his contribu- 
 tions to the advancement of chemistry. 
 
 Dalton lived until 1844, but his classical memoirs practically 
 all belong to the period before 1815. 
 
KESEAECHES UPON THE RATE OF EXPAN- 
 SION OF GASES AND VAPORS. 
 
 BY L. J. GrAY-LuSSAC. 
 
 From the Annales de CMmie, series 1, volume 43, pages 137 
 175 (1802). Translated into German, Gilbert's Annalen, vol- 
 ume 12, pages 257291 (1802). 
 
CONTENTS. 
 
 PAGE 
 
 Object of the investigation .... . . 27 
 
 Effect of the presence of moisture upon the expansion of 
 
 29 
 
 Earlier investigations : 
 
 Amontons . . . . .30 
 
 Nuguet , . ' . . .31 
 Lahire =v - . -31 
 
 Stancari . . . . . . . . .32 
 Colonel Roy ... 
 
 Saussure 33 
 
 Priestley ... 
 
 Monge, Berthollet and Vandermonde . .34 
 
 Guy ton de Morvean and Duvernois . .35 
 
 Charles ....-,. . . 37 
 
 Apparatus and manipulation : 
 
 First Method . . . - ... 38 
 
 Same, simplified . . 
 
 Results with air ... ^2 
 
 Results with other gases . 43 
 
 Method employed for gases soluble in water . 
 
 Results 45 
 
 Experiments upon ether vapor . . .47 
 
 Conclusions .48 
 
 Biographical Sketch . . 
 
 26 
 
RESEARCHES UPON THE RATE OF EXPAN- 
 SION OF GASES AND VAPORS. 
 
 BY L. J. GAY-LUSSAC. 
 
 PAKT I. 
 Object of this Memoir. 
 
 FOR a long time physicists have busied themselves with [the 
 problem of] the expansion of gases; but their researches pre- 
 sent such great discrepancies in the results that, instead of 
 establishing their views, they call, on the contrary, for a more 
 rigorous investigation. 
 
 The expansion of vapors has attracted the attention of physi- 
 cists to a less extent. Although for a long time the extraordi- 
 nary properties of steam have been recognized and the most 
 beneficent applications of them have been brought about, 
 Ziegler and Bettancourt are the only ones, to my knowledge, 
 who have endeavored accurately to determine them. Their 
 experiments cannot however lead to a knowledge of the actual 
 expansion of this vapor; since', having always somo water in 
 their apparatus, there was, for each new degree of heat, an 
 expansion of the vapor produced by former increments of heat 
 and an increase of volume due to the formation of new vapor 
 two causes which combined evidently to push up the mercury 
 in their manometer. 1 
 
 1 The apparatus of Bettancourt consists of a boiler of copper with 
 a cover of the same metal, through which three tubes pass. The first 
 serves to introduce water into the boiler; through the second is inserted 
 the stem of a thermometer intended to show the temperature of the 
 vapor, and to the third is attached a suitably shaped barometer tube to 
 measure the tension of this same vapor. A vacuum is produced in the 
 boiler with the aid of a pneumatic pump, which is connected by means 
 of a tube provided with a stop cock. The apparatus of Ziegler differs 
 but little from that of Bettancourt; but Ziegler not having produced, as 
 Bettancourt did, a vacuum in his boiler, there results a great difference 
 in their experimental data. (Architecture hydraulique de Prony, Tome 
 II). 
 
 27 
 
MEMOIRS ON 
 
 The thermometer, as it exists to-day, cannot serve to show 
 with accuracy relative amounts of heat, because we do not yet 
 know what relation exists between the degrees of the ther- 
 mometer and the quantities of heat which they can indicate. 
 We believe, it is true, in general, equal divisions of its scale 
 correspond to equal increments of caloric; but this view is 
 supported by no very positive fact. 
 
 It must therefore be admitted that we are far from having 
 exact knowledge of the expansion of gases and vapors and of 
 the movements of the thermometer; and in the meantime 
 there is every day a call, in physics and in chemistry, to reduce 
 a given volume of gas at one temperature to another; to meas- 
 ure the heat given off or absorbed in the change of constitution 
 of substances, that given off or absorbed by the same body in 
 passing from one temperature to another; in the arts, in calcu- 
 lating the efficiency of steam engines, in ascertaining the rate 
 of expansion of many substances; in meteorology, in deter- 
 mining the quantity of water held in solution in the air a 
 quantity which varies with its temperature and its density and 
 follows a law as yet unknown. Finally, in the preparation of 
 tables of refraction by astronomers and in the application of the 
 barometer to the measurement of altitudes, it becomes indis- 
 pensable to know with accuracy the temperature of the air and 
 the law of its expansion. 
 
 Although these facts have made it very desirable to engage 
 in a work of such general application, the difficulty of the 
 investigations which it demands would have prevented my de- 
 voting myself to it, had I not been on the other hand strongly 
 urged by Citizen Berthollet, whose pupil I have the honor to be. 
 To him I owe the means necessary for the prosecution of this 
 research, during which I have often been assisted by his advice 
 and by that of Citizen Laplace: men whose reputation will add 
 to the confidence my work would inspire. 
 
 The researches I have undertaken upon the law of the ex- 
 pansion of gases and vapors, and upon the movements of the 
 thermometer, not being yet complete, I have for my object in 
 this memoir only to investigate the expansion of gases and 
 vapors for one definite rise of temperature and to make it clear 
 that this is the same for all these fluids; but before giving an 
 
 28 
 
EXPANSION OF GASES 
 
 account of my experiments, I think I ought to give an histori- 
 cal survey of what has been done upon this subject. And as 
 I add at the same time some comments upon the means which 
 have been employed, I intend to preface them with a discus- 
 sion of one of the chief causes for uncertainty which can 
 enter into this class of investigations. Although it is very 
 important and although it seems to have been unknown to 
 the majority of the physicists who have studied the expansion 
 of gases, it will be enough for me merely to state it to make 
 its influence felt. What I say of atmospheric air will apply to 
 other gases. 
 
 This cause of uncertainty is due to the presence of water in 
 the apparatus. As a matter of fact if a few drops of this fluid 
 are left in a vessel filled with air whose temperature is then 
 raised to that of boiling water, this water, on passing into the 
 form of a vapor, will occupy about 1800 times as great a volume 
 as at first, and by this means will drive out a very large part of 
 the air originally enclosed in the vessel. It necessarily follows 
 that when this vapor is condensed and therefore occupies a 
 space 1800 times as small we should ascribe to the air remain- 
 ing in the vessel an expansion far too great; for it would be 
 assumed that it was this air which at the temperature of boiling 
 water filled all the space in the vessel. If we do not carry the 
 temperature up to this point, the same source of inaccuracy 
 will nevertheless exist, and its extent will be proportional to 
 the temperature at which we stop: for in this case the water 
 will not all evaporate, but the air will dissolve more and more as 
 the temperature rises and will consequently assume a greater and 
 greater volume over and above that which it owes to the heat; 
 so that when we pass to a lower temperature the volume of air / v 
 which fills all the space in the vessel will decrease from two 
 causes: (1) through the .loss of its caloric, (2) through that of 
 the water which it holds in solution. Too great an expansion 
 would thus be assumed for the air. 
 
 Speaking generally, whenever there is enclosed with gases 
 any liquid, or even any solid which like sal ammoniac, for 
 example, can be dissolved or become vaporized at the tempera- 
 ture to which it is to be raised, errors must of necessity result 
 in the determination of the expansion of these gases. 
 
 29 
 
MEMOIRS OX 
 
 PART II. 
 
 Historical Sketch of what has been done upon the 
 Expansion of Gases. 
 
 The expansion of atmospheric air by heat was well known 
 before the time of Amontons, but this physicist is apparently 
 the first to seek to determine its amount for a given rise of 
 temperature. To attain this result he enclosed some air with 
 the aid of mercury in a flask connected with one of the arms 
 of a reversed siphon, and placed this apparatus in a bath of hot 
 water. 1 The air expanded by the heat presses upon the mer- 
 cury and forces it into the other branch of the siphon; so that 
 he judged, by the height of the mercury compared with its 
 level in the flask, the tension the air had reached. 
 
 From various experiments made upon different volumes of 
 air, he concludes (Mem. de I'acad., 1699, 1702): (1) "That the 
 heat of boiling water has limits which it does not pass; (2) 
 that various volumes of air increase their tensions at the same 
 rate for equal degrees of heat, and vice versa; (3) that the heat 
 of boiling water increases the tension only until it is capable 
 of sustaining about the weight of a column of mercury of ten 
 inches' height/' 
 
 It appears then that, however compressed a volume of air 
 may be, the heat of boiling water always increases its tension 
 one third; that is to say, a volume of air compressed, for 
 example, under a column of 60 inches of mercury, including 
 the weight of the atmosphere, will support, at the temperature 
 of boiling water, a column of mercury of about 80 inches. He 
 therefore concludes "that the same degree of heat, small as it 
 may be, will always increase the tension of the air more and 
 more as this air is supporting a greater and greater weight/' 
 
 If Amontons had started from a degree of heat more clearly 
 defined than what he calls an average, which would have been 
 at that time scarcely possible it would have been possible to 
 calculate from his experiments with sufficient approximation 
 
 1 The air enclosed in the flask, not being able to escape when the 
 mercury is poured in, is a little more compressed than it would be 
 naturally; but if no other pressure than that of the atmosphere is de- 
 sired, it would be very easy to avoid this slight inconvenience. 
 
 30 
 
EXPANSION OF GASES 
 
 the expansion of atmospheric air; yet, since he conducted his 
 comparisons with volumes of gas of very unequal density, one 
 may conclude from them that, however dense a volume of air 
 may be, the increase of elasticity which this air acquires for the 
 same degree of heat always bears the same relation to that which 
 it had prior to the experiment. 
 
 Nuguet, in seeking to verify the results of Amontons, ob- 
 tained others entirely unlike them. In one of his experiments, 
 the volume of the air expanded by the heat of boiling water 
 and the original volume were to one another as 2 to 1, and in 
 two other experiments as 16 to 1. His apparatus consisted of a 
 flask inverted and sunk in a water bath whose temperature he 
 raised to that of boiling water. It is evident that this appara- 
 tus was extremely defective, since the air in it was always in 
 contact with water; and Nuguet had in addition let some 
 water into his flask. It is not surprising, therefore, that he 
 obtianed results so discordant and, so to speak, so extraordin- 
 ary. (Mem. de I'acad., 1708. Lahire.) 
 
 This great difference between the results of Amontons and 
 those of Nuguet upon the rate of expansion of atmospheric 
 air, and the realization that it had been subjected to experi- 
 ment under conditions which were not usual, led Lahire to ap- 
 ply himself to the same problem. The apparatus of which he 
 made use was identical with that of Amontons, except that the 
 bulb carried a small tube which he sealed after having intro- 
 duced the mercury. By this means, the mercury being at the 
 same level in the bulb and in the syphon, the air which he sub- 
 jected to experiment was no more compressed than the sur- 
 rounding air. With this apparatus Lahire found, first, in one 
 experiment that the air expanded from an average temperature 
 up to that of boiling water, could not sustain a column of mer- 
 cury of one third of the weight of the atmosphere; later, he 
 found in another, the thermometer being lower and the barom- 
 eter higher than in the former experiment, that the air, ex- 
 panded by the heat of boiling water, could not support a col- 
 umn of mercury so high as the former one. These two results 
 are evidently contradictory; but Lahire suspected no error and 
 drew the conclusion from them that we are bound to admit 
 that we do not yet know the nature of the air. 
 
 31 
 
MEMOIRS ON 
 
 In order to explain the great difference which existed be- 
 tween his results and those of Nuguet, a difference far too 
 great not to be due to some outside influence, Lahire noticed 
 that Nuguet had let a little water into his apparatus; and from 
 this fact he concluded that it might be this water which, on be- 
 ing converted into vapor and expelling a large part of the air 
 enclosed in the flask, had produced so great an expansion. He 
 was thoroughly confirmed in his opinion by the result of an ex- 
 periment carried out after Nuguet's method, in which he let a 
 little water into the flask; for he found that the volume of the 
 air expanded from the average temperature up to that of boil- 
 ing water, and the original volumes were to one another as 35 
 is to 1. (Mem. de I'acad., 1708.) 
 
 At the same time M. Stancari of Bologna showed that water 
 increases to a considerable degree the volume of air at a tem- 
 perature but slightly raised. We therefore owe to these two 
 physicists the important discovery of the influence of water up- 
 on the expansion of atmospheric air; yet although they have 
 by their experiments given the matter prominence, it has since 
 been generally overlooked. To the slight attention paid to 
 this influence must be ascribed the great divergencies found in 
 the results of physicists upon the expansibility of gases. 
 
 It is known that the altitudes to which one ascends in the 
 atmosphere are given by the logarithms of the corresponding 
 heights of the barometric column. If the density of the air were 
 always the same, it would be easy thus to calculate the alti- 
 tude of one place above another stated place, by observing the 
 barometer there. It would therefore be important to distin- 
 guish the causes that affect the density of the air, in order to 
 make the necessary corrections in the heights given by the ba- 
 rometer. 
 
 Deluc, who has inaugurated a new era in this department of 
 physics, recognized in heat one of these causes. In order 
 clearly to identify its effect, he began by endeavoring to fix the 
 temperature at which the logarithms indicate directly the cor- 
 rect altitudes, and found, on comparing numerous observations 
 made at places whose altitudes he had determined with accur- 
 acy, that this was the case at the temperature of 16f of the 
 thermometer graduated in 80 divisions, and this he calls tem- 
 
 32 
 
EXPANSION OF GASES 
 
 perature fixe. Therefore to make correction for the effects of 
 heat above and below this fixed point, he again compared the 
 altitudes found from the logarithms with those he had meas- 
 ured, attributing to heat the variations of the first from the 
 second, and drew the conclusion that "in the neighborhood of 
 the fixed temperature, the correction for one degree of the 
 thermometer would be to the altitude of the place as 1 is to 
 215." (Recher, sur Us modif. de Vat., IV Part, Ch. III.) 
 
 Colonel Roy has found a far greater rate of expansion for 
 air. According to him, in the neighborhood of 15 on a ther- 
 mometer graduated in 80 divisions, air expands T ^ of its vol- 
 ume for each degree. He also found that moist air expands 
 much more than dry air; but Saussure noted that in carrying 
 out his experiments, Col. Roy had admitted into his manome- 
 ter either water in a liquid state or water vapor and had con- 
 fused two things which should be distinguished, namely, the 
 conversion of water into an elastic fluid, and the expansibility 
 of air mixed with this vapor. (Philos. transact., 1777, p. 704.) 
 
 Saussure determined the rate of expansion of air in the neigh- 
 borhood of 6 to be yfa of its volume for each degree. His ex- 
 periments were performed with a large flask in which were 
 enclosed a thermometer and a barometer to indicate the varia- 
 tions of the temperature of the air and the corresponding ten- 
 sion acquired. In order to study the effect of water upon the 
 expansion of air, he enclosed in his flask air of varying degrees 
 of dryness, avoiding the formation anew of vapor, and, far from 
 finding this air more expansive than very dry air, he thought he 
 had discovered, on the contrary, that very dry air was even a 
 little more expansive than air which was very moist, but was 
 holding its moisture all the time entirely uncondensed. (Es- 
 sai sur I'hygrometrie, page 1 08.) 
 
 Up to this time physicists had limited themselves to the ex- 
 pansion of atmospheric air, and the first to occupy himself with 
 that of other gases is the celebrated Priestley. He proceeded 
 as follows : 
 
 After having filled a flask, over mercury, with the gas he 
 wished to test, he fitted to it a bent tube, one of whose arms was 
 nearly horizontal, and left a little mercury in the neck of the 
 flask so that the expansion of the gas could push it into the 
 
 33 
 
MEMOIRS ON 
 
 tube. This done, he put his apparatus in a small wooden box, 
 introduced a thermometer, and carried it into rooms at differ- 
 ent temperatures : the expanded air caused the mercury to 
 move a greater or less distance along the tube, and it was by 
 this distance measured in inches that Priestley determined the 
 expansibility of different gases. As all the experiments were 
 made with the same flask and the same tube, which he probably 
 inclined always in the same way, they give a ratio among the 
 expansibilities of different gases, but not the actual expansion ; 
 for it would be necessary to know for that purpose the volume 
 of that part of the tube traversed by the mercury in compari- 
 son with that of the flask, and to know, in addition, the exact 
 inclination of the tube, of which Priestley makes no mention. 
 I shall not pause longer to discuss these experiments ; all the 
 more as Priestley himself did not put much confidence in them 
 and wished to repeat them under better conditions. Assuming 
 the volumes of the different gases equal, the expansion measured 
 in inches along the tube, for 4.44 of the thermometer gradu- 
 ated in 80 divisions, 1 would be : 
 
 Ordinary air . . . . . 1.32 inches 
 Hydrogen gas . . . . . 2.05 " 
 Nitrous gas ... . . 2.02 " 
 Carbonic acid gas . . . . 2.20 " 
 Muriatic acid gas ... . . 1.33 
 Oxygen gas ' .' . . . 2.21 
 
 Nitrogen gas 1.65 
 
 Sulphurous acid gas .... 2.37 
 
 Fluoric acid gas 2.83 
 
 Ammoniacal gas . .. .- . . 4.75 
 
 (Experiments and Observations, etc., Boole VII, Section VI.) 
 In a memoir printed among those of the Academy for the 
 year 1786, Citizens Monge, Berthollet and Vandermonde have 
 concluded from an experiment that, for one degree atmospheric 
 air expands T W.^s f ^s volume, and hydrogen gas rffi.ff*- 
 
 Lastly, Citizen Guyton, realizing how little accord there was 
 on [the subject of] the rate of expansion of atmospheric air, 
 
 1 Note by Translator: On an 80-degree thermometer scale (e. g. 
 Reaumur's) 4.44 is the equivalent to 10 Fahrenheit. The latter was 
 evidently the temperature interval employed by Priestley. 
 
 34 
 
EXPANSION OF GASES 
 
 and that there were still no direct experiments on record which 
 determined the expansion of gases for slightly elevated degrees 
 of heat and for successive degrees near together, undertook, 
 with Citizen Duveriiois, to throw some light upon this matter. 
 As their work is the most recent, I shall pause a moment to 
 endeavor to show what the causes are which were able to affect 
 their result. 
 
 Their apparatus consisted of a flask fitted with a bent tube 
 by means of which the air expelled from the flask by heat was 
 caught in a receiver in the mercury trough. The flask, full of 
 the gas they wished to subject to experiment, was immersed in 
 a bath at the temperature of melting ice and was held there 
 by an iron cover. They heated the bath to 20, 40, 60% 80, 
 successively, and caught in different receivers the gas forced 
 out by expansion through each of these intervals; they finally 
 determined the volumes of air escaping from the flask by 
 measuring them in their respective receivers after having 
 reduced them to the temperature of melting ice, and thus 
 found the volume of that remaining in the flask. 1 But apart 
 from the fact that their apparatus made it necessary for them 
 to determine many constants which must interfere with the 
 accuracy of their results I note that, after the sinking of the 
 bent tube in the mercury, not having introduced some more 
 air into the flask to replace the mercury which was pushed into 
 the tube as a result of the pressure of the mercury of the bath, 
 several degrees of heat would be needed before a single bubble 
 of air escaped from the flask; so that, if they had made use of 
 lesser intervals, as, [for example] of 5 each, they would have 
 found that, starting from zero, the first degrees of heat would 
 have shown no expansion in the different gases. Indeed they 
 have observed an expansion for the first 20 degrees which, for 
 the majority of the gases, is far too small. 
 
 This source of error, although serious, would not have car- 
 ried the results of Citizens Guyton and Duvernois so wide of 
 the truth, had there not been others still more serious. Thus 
 I suspect that their flask had not been properly dried and that 
 a little water may have got in during the introduction of the 
 
 1 Annales de Chimie, Vol. I. 
 
 35 
 
MEMOIRS ON 
 
 gases. Had a decigram of water remained, it would have 
 served to aUect their results iu a marked way, especially towards 
 the higher degrees, where, in changing into an elastic fluid, it 
 would have forced a large part of the air out of the flask. 
 
 In this way can be explained the noticeably increasing pro- 
 gression which they have determined for all the gases, whereas 
 they ought to have found a decreasing one, on lowering to the 
 temperature of melting ice the amount forced out by each 
 expansion. I note in connection with this point, that Citizen 
 Guy ton expresses himself as regards the expansion of hydrogen 
 gas as follows: 1 " The four [volumes] resulting from the expan- 
 sion were caught this time in a receiver which had been sur- 
 rounded with vessels filled with ice. In spite of this, the 
 mercury of the little trough showed upon the thermometer [a 
 temperature] 2, 3, 4, 6 degrees above zero, while the water of 
 the bath was at the same moment at 20, 40, 60, and 80 degrees 
 a thing which could produce some inaccuracy in the deter- 
 mination of each of these quantities, but which cannot be of 
 much consequence, the expansion being very slight through 
 these first degrees." 
 
 From this one may conclude that these physicists gave no 
 more care to reducing the volumes of the other gases to zero; 
 and, if this be the case, there results another source of uncer- 
 tain ty Q in their experiments. 
 
 In comparing the volumes of gas left in the flask with those 
 that had been driven out by heat, Citizens Guyton and Duver- 
 nois have found that the gases oxygen, hydrogen, carbonic acid 
 and atmospheric air had shown a contraction and have given 
 as its cause combinations which had taken place during the 
 time of the experiments. Employing mercury which was very 
 pure and free from oxide, I have been unable to detect any 
 noticeable action between the metal and these gases from the 
 temperature of melting ice up to that of boiling water. 
 
 Below is a table of the results of Citizens Guyton and 
 Duvernois ; they have enclosed between parentheses those in 
 which they have little confidence. 
 
 l Annales de Chimie, T. I, page 284. 
 
 36 
 
Wtw wvisrow 
 
 EXPANSION OF GASES 
 
 From 
 
 to 20 
 
 From 20 
 to 40 
 
 From 40 I From 60 I From 
 
 to 60 to 80 to 80 
 
 Ordinary air 
 expands 
 
 Vital air 
 Nitrogen gas 
 Hydrogen gas 
 
 Nitrous gas 
 
 Carbonic 
 
 acid gas 
 
 Ammoniacal 
 
 gas 
 
 [s.fcy) T.itaT 
 
 'r.W | (3 + y.W) 
 
 T.V* 
 
 Mn) 
 
 .W 
 
 .V 
 
 s.r 
 
 T.W 
 
 Before going further, I ought to say that, although I had 
 noted a great many times that the gases oxygen, nitrogen, 
 hydrogen, carbonic acid and atmospheric air expand to the 
 same extent from to 80, Citizen Charles had, fifteen years 
 before, discovered the same property in those gases ; but, never 
 having published his results, it was by the greatest chance that 
 I learned of them. He had also endeavored to determine the 
 rate of expansion of gases soluble in water and had found for 
 each a characteristic rate of expansion different from that of 
 the other gases. In respect to this my conclusions differ much 
 from his. 
 
 Citizen Charles employed as his apparatus a barometer the 
 chamber of which was of a large size. The gas which he wished 
 to submit to experiment was enclosed in the reservoir of the 
 barometer at the temperature and under a pressure of 28 
 inches of mercury. When this barometer was submerged in 
 boiling water, the mercury rose in the tube and the excess of 
 the entire column over that of 28 inches indicates the tension 
 the gas had acquired ; but Citizen Charles having been kind 
 enough to show me the apparatus, I saw that the tube of the 
 barometer was very large in proportion to the capacity of the 
 reservoir ; so that the rise of the mercury above 28 inches did 
 not show all the tension the gas had acquired, since for that it 
 would be necessary that its volume in the reservoir had 
 remained constant. It therefore seems to me that the true 
 
 37 
 
MEMOIRS ON 
 
 rate of expansion of gases cannot be deduced from these ex- 
 periments. 
 
 PAKT III. 
 
 Description of Apparatus. 
 
 A flask B (Fig. 1) is provided with an iron tap to which a 
 bent tube ID (See Fig. 2) can be fitted. The key of the tap 
 carries a lever LL pierced at its two ends to receive two cords 
 by which one can open and close the tap under water. 
 
 FIG. 1 
 
 To introduce gases into the flask, I made use of a glass bell 
 jar M (Fig. 1), to which are fitted a tap and a bent tube T, 
 and sunk in a vessel QS. On pouring water into the vessel 
 and opening the tap, the gas compressed in the bell jar escaped 
 by the tube and filled the flask B placed mouth-downward in 
 the mercury bath PO. When the flask is full, I close the tap, 
 adjust the tube ID (Fig. 2) and fix it in a cylindrical iron cage 
 EFGH, which I then place in a copper vessel AD, full of 
 water. In order that there might be no communication between 
 the outside air and the gas enclosed in the flask when the tap 
 is opened, I lowered the end of the tube ID one or two 
 millimeters into the small mercury bath KX. This done, I 
 heat the bath and at intervals of 10, let us say, open the tap 
 and immediately close it again. The gas, tending to expand 
 
 38 
 
EXPANSION OF GASES 
 
 on account of the heat, escapes rapidly from the flask and has 
 soon driven out the atmospheric air which filled the tube ; 
 from 40 on the tap can with safety be left open until the end 
 of the operation : I prefer however alternately to open it and 
 close it, as I find that [under these circumstances] the gas in 
 the flask comes more rapidly to the temperature of the bath. 
 After 15 or 20 minutes of boiling a sufficient time for every- 
 
 HORIZONTAL SECTION 
 ON YZ 
 
 A\ 
 
 FIG. 2. 
 
 thing to come to the same temperature I remove the end of 
 the tube ID from the mercury, in order to secure equilibrium 
 between the outside air and the gas in the flask, and then close 
 the tap. After having cooled the bath with ice or water, I 
 remove the apparatus, disconnect the flask from which I 
 remove the tube ID and also the lever LL and submerge it 
 completely in a bath of known temperature where I leave it 
 long enough for it to come perfectly to that temperature. 
 
 Now, on opening the tap, there enters the flask a volume of 
 water which is exactly equal, when equilibrium is restored, to 
 that of the gas which has been driven out by the heat. The tap 
 
 39 
 
MEMOIRS ON 
 
 being closed, I remove the flask, carefully dry its surface and 
 weigh it in this condition ; afterwards I weigh it full of water 
 and empty, recording the results of each weighing. These 
 being known, I find the volume of the flask by subtracting the 
 weight of the empty flask from that of the flask filled with 
 water, and the volume of the water which represents the volume 
 of air driven out of the flask by the heat, by subtracting, again, 
 the weight of the empty flask from that of the flask when it 
 contained this water. It will thus be very easy to determine 
 the relationship between the original volume and the volume 
 when expanded. 
 
 This method has the advantage of possessing great accuracy; 
 
 for, as the volumes are found from the weights, the error 
 
 which can be made in this determination must be very small, 
 
 even when use is made of balances of no great sensibility. 
 
 The apparatus I have described is simple enough in itself, 
 
 yet, as it calls for the use of ce- 
 ments and of a tap which must 
 be of iron by reason of the mer- 
 cury, its manipulation is some- 
 what difficult. It will not there- 
 fore be out of place to describe 
 another apparatus also which I 
 have used and which, along with 
 great simplicity and easy manipu- 
 lation, possesses at least nearly 
 advantages of the former one. 
 It is a simple flask D (Fig. I, Plate II) 
 [See Fig. 3] whose neck must be at least 
 a decimeter long. After having filled it 
 with the gas I wish to subject to experi- 
 ment, in the way already described, I in- 
 troduce its neck about two centimeters 
 into the mercury contained in an ordinary 
 vessel OM, and fasten it in an iron frame 
 as in the case of the former apparatus. 
 If I immerse it in this condition in a bath of hot water, the gas 
 expanded by the heat, in order to escape, will have to overcome, 
 not only the pressure of the mercury in the vessel, but that of 
 
 40 
 
EXPANSION OF GASES 
 
 the water of the bath as well. To do away with this incon- 
 venience, I introduce into the neck of the flask the end of a 
 very narrow bent tube B, taking care to keep the end G closed 
 until it has been lowered into some mercury. To support the 
 tube, I fasten to the middle of it a cord on the end of which I 
 hang a weight and pass it over a support, in. such a way that 
 the weight by its action tends to lift the tube. The apparatus 
 being thus arranged, I place it in a glass tank where there is a 
 depth of water equal to that which should be in the bath, I 
 open for a moment the end of the tube in order to establish 
 equilibrium with the pressure of the outside air, and close it 
 again at once. As there is a scale whose divisions are very 
 small upon the neck of the flask, I read the exact level of the 
 mercury ac inside the neck of the flask and record it, since it 
 is to this level that the volume of the flask extends. The end 
 of the tube B must be raised above the level ac, for otherwise 
 the mercury will enter the tube and offer a resistance to the 
 escape of the gas expanded by the heat. After all these ma- 
 nipulations which take longer to describe than to carry out 
 I place the apparatus in a bath of hot water and open the end 
 of the tube G after having put it in a small mercury bath, as 
 in the former apparatus. When the flask has come to the tem- 
 perature of the boiling water, I remove the tube B (whose end 
 must have been previously withdrawn from the mercury), and 
 cool the bath. The mercury then rises in the flask ; but it will 
 be easy to put water in its place, when everything is at a lower 
 temperature. The volume of the flask and the volume of the 
 water which has taken the place of that part of the gas driven 
 out by the heat, are found in the way I have already described ; 
 only it is necessary in this calculation to add to the weight of 
 the empty flask that of the cylinder of water extending from 
 the level ac on the one hand to the end of the neck of the 
 flask on the other. 
 
 I should be able to give still further details, but I withhold 
 them in order not to be too diffuse : those a little practiced in 
 manipulation will readily supply them. However, as it is a mat- 
 ter of importance, after what I have said about the effects of 
 moisture, to remove it entirely from the apparatus, I will de- 
 scribe how I have been successful in doing so. 
 D 41 
 
MEMOIKS ON 
 
 If the flask is evidently wet, I begin by drying it with filter 
 paper ; then I heat it so as to evaporate a part of the moisture 
 which it still may contain, and, with the aid of a bellows to 
 which I have attached a glass tube, I carry into its interior a 
 current of air to drive out the vapor. These last operations 
 being repeated many times with the flask and the tube, both 
 become perfectly dry. With regard to the mercury which I 
 have used in my experiments, I have invariably used what was 
 very dry and pure. 
 
 In all the experiments the results of which I am about to 
 give, I have always brought back to the temperature of melting 
 ice the gases whose rate of expansion I have been able to de- 
 termine with the apparatus I have described ; and for this pur- 
 pose I had a bath where I kept the ice and in which the flask 
 was completely covered after having been taken from the bath 
 in which it had been subjected to experiment, and here I left 
 it for about half an hour, during which time I constantly stirred 
 the bath. The other fixed temperature which I resolved upon 
 for the same gases, is that of boiling water. 
 
 I have made some experiments at other temperatures ; but 
 they will have to be repeated, and moreover they will become 
 part of a treatise which I have begun upon the law of the ex- 
 pansibility of gases and vapors ; I shall confine myself there- 
 fore, as I have said, to a consideration of the rate of expansion 
 of gases for a definite rise of temperature which will be that 
 comprised between the degree for melting ice and that for boil- 
 ing water. With respect to vapors, I shall compare their rate 
 of expansion with that of gases. 
 
 PART IV. 
 
 Experiments and Results. 
 
 MAKING use of the two [forms of] apparatus I have de- 
 scribed but more often the second than the first and avoid- 
 ing all the sources of inaccuracy which I could foresee, I have 
 found from six experiments upon atmospheric air, the six fol- 
 lowing results : * 
 
 1 My flask held about 350 grams of water. 
 
 42 
 
EXPANSION OF GASES 
 
 Starting from the temperature of melting ice, at that of 
 boiling water equal volumes of atmospheric air represented by 
 100 had become, respectively : 
 
 137.40 ; 137.61 ; 137.44 ; 137.55 ; 137.48 ; 137.57 ; 
 the mean of which is nearly 137.50. 1 
 
 If the total increase of volume be divided by the number of 
 degrees which produced it, or by 80, we find, making the 
 volume at temperature equal to unity, that the increase of 
 volume for each degree is * T ira or on tne other hand, ^.^ 
 for each degree of the centigrade thermometer. 
 
 Deluc having found ^J y for the coefficient, it would appear 
 at first sight that our results are the same ; but if it be noted 
 that he starts from a temperature of 16f , while I start from 
 a temperature of 0, it will be seen that our results are quite 
 different. 2 I shall later consider this difference and show 
 that the coefficients of expansion vary with the temperature 
 from which we set out. 
 
 Hydrogen gas produced from iron by weak sulphuric acid 
 was submitted to two experiments : in one, through an eleva- 
 tion of temperature from that of melting ice to that of boiling 
 water, 100 parts [by volume] became 137.49 ; and in the other, 
 through the same rise of temperature 100 parts became 137.56. 
 The average of these two results is 137.52 which differs only 
 slightly from the average result found for the expansion of 
 atmospheric air. 
 
 Oxygen gas given off from the oxygenated muriate of 
 potash [i. e., potassium chlorate] was tested three times and 
 gave the following results : 100 parts became 
 
 1 Although the differences among the results are not very consi- 
 derable, I believe I could have made them very small had I been able to 
 note the state of the barometer during the boiling of the water. How- 
 ever, I have always taken care to note its temperature at the moment 
 of boiling and I confess I have never noticed any marked variations. 
 As a matter of fact it requires a change of an inch in the barometer to 
 produce one of a degree in the boiling point of water, which must 
 occur but rarely. However that may be, the mean result, 137.50, must 
 be very close. 
 
 2 Note by Translator: In the memoir the second temperature stated 
 is " 0| ; " it seems evident that this is a typographical error. 
 
 43 
 
ME MO IKS ON 
 
 137.47 ; 137.54 ; 137.45 ; 
 the mean of which is 137.48. 
 
 Nitrogen gas obtained through the decomposition of am- 
 monia by oxygenated muriatic acid [i. e. chlorine] gave the fol- 
 lowing five results : 100 parts became 
 
 137.42 ; 137.56 ; 137.50 ; 137.46 ; 137.55 ; 
 the mean of which is 137.49. 
 
 On bringing together the preceding results and comparing 
 the expansion of the gases oxygen, hydrogen and nitrogen with 
 that of atmospheric air, there results a table like this 
 
 Between the temperature of 
 melting ice and that of boil- 
 ing water, 100 parts of 
 
 Suffer an 
 increase of 
 
 Differences 
 
 Atmospheric air 
 Hydrogen gas 
 Oxygen gas 
 Nitrogen gas 
 
 37.50 parts 
 37.52 
 37.48 
 37.49 
 
 + 0.02 
 0.02 
 0.01 
 
 The slight differences observable in the above results may 
 arise from the fact that it is impossible to make the conditions 
 rigorously identical in every experiment, and as they amount to 
 only two ten-thousandths of the original volume, we may safely 
 conclude that atmospheric air and the gases oxygen, hydrogen 
 and nitrogen expand to the same extent between the tempera- 
 ture of melting ice and that of boiling water. 
 
 In order to determine the rate of expansion of gases soluble 
 in water, I made a change in the apparatus. I used two tubes 
 TT(Fig. 2, Plate II) [See Fig. 4] calibrated at the same time 
 over the same mercury bath AC, by means of a very small 
 measure. 
 
 Each time that I made use of this apparatus, I took care 
 that the quantity of mercury should be the same as when the 
 tubes were calibrated. I ought to say that, if the basin which 
 held the mercury suffered any injury, it was necessary to re- 
 calibrate the tubes for another bath ; indeed it would be well to 
 cut them from the same cylinder of glass and to give them the 
 same height, in order to have all the conditions as much the 
 same as possible. 
 
 Into one of these tubes I admitted atmospheric air down to 
 
 44 
 
EXPANSION OF GASES 
 
 the 100th division, for example, and into the other the gas 
 whose rate of expansion I wished to determine, also as far as the 
 100th division. I thus subject to test 100 equal measures of 
 each of two gases. I then place the apparatus in a heater 
 whose temperature I can control and watch the progress of the 
 expansion of the gases. However great the care I have taken to 
 observe closely, I have never 
 perceived any difference and 
 have always noticed that the 
 same divisions were passed at 
 the same time in the two tubes. 
 
 The gases I have thus ex- 
 amined have never been intro- 
 duced directly into the tubes; I 
 have kept them for some time 
 before in an intermediate vessel 
 in which I put some drying- 
 agent, for example, muriate of 
 lime, [i. e. calcium chloride] 
 and made them pass thence into 
 the tubes by compressing them 
 with the aid of mercury which I 
 introduced by means of a safety 
 tube fitted to the intermediate FIG. 4. 
 
 flask. If these precautions are neglected, there will almost 
 always result far too great an expansion ; we must therefore 
 avoid the contamination of unabsorbed moisture or of any 
 other substance capable readily of assuming the gaseous state. 
 
 100 measures of carbonic acid gas obtained from marble 
 with the aid of sulphuric acid were compared with 100 measures 
 of atmospheric air. From the fifth degree up to the 90th de- 
 gree the expansions were the same in the two tubes. 
 
 100 measures of muriatic acid gas produced with the aid of 
 concentrated sulphuric acid from muriate of soda [i. e. com- 
 mon salt] thoroughly dried by heat, having been compared 
 with 100 measures of atmospheric air from the 3d degree up to 
 the 86th, the expansions of the two gases were absolutely the 
 same. This experiment, as well as the preceding one, was re- 
 peated many times, and always gave the same result. 
 
 45 
 
MEMOIES OK 
 
 Sulphurous acid gas and nitrous gas, again, showed under 
 the influence of heat the same expansion as atmospheric 
 air. 
 
 Dr. Priestley and Citizens Guyton and Duvernois have found 
 very great expansibility in the case of ammonia gas. With tiie 
 idea of discovering the cause which was capable of vitiating 
 the results of their experiments, I introduced directly into one 
 of the tubes some ammonia gas produced by the decomposition of 
 muriate of ammonia by means of ordinary lime, and into the 
 other a suitable volume of atmospheric air. As the tempera- 
 ture rose, the ammonia gas expanded proportionally more than 
 the atmospheric air, in fact to such a degree as soon to become 
 twice as great; yet on examining the mercury surface and the 
 walls of the tube, after lowering the temperature, I noticed a 
 trace of liquid and some crystalline needles which could be 
 only muriate or carbonate of arnmonia ; and the whole disap- 
 peared on raising the temperature to a sufficient degree. How- 
 ever that may be, I began the experiment again by allowing 
 the ammonia gas to stand some time in an intermediate flask 
 where there was some caustic potash, and then, from up to 
 95, its expansion followed exactly that of atmospheric air. I 
 again examined the surface of the mercury and the walls of the 
 tube, when the temperature had returned to 0, but this time 
 I noticed neither liquid nor crystalline needles. This experi- 
 ment, repeated many times, always met with the same suc- 
 cess. 
 
 It is thus evident, from what I have said, that not only a liq- 
 uid, but any other substance capable of assuming the gaseous 
 state can easily lead to error; it is necessary therefore to avoid 
 such things with the most scrupulous care. 
 
 The experiments of which I have given an account and all of 
 which were made with great care, prove without a doubt that 
 atmospheric air and the gases oxygen, hydrogen, nitrogen, nit- 
 rous gas, ammonia, muriatic acid, sulphurous acid and car- 
 bonic acid gases expand to the same extent for the same de- 
 grees of heat; and that consequently their greater or less dens- 
 ity under the same pressure and at the same temperature, their 
 greater or less solubility in water, and their individual charac- 
 ter, have no influence upon their expansibility. 
 
 46 
 
EXPANSION OF GASES 
 
 In consideration of this fact I conclude that all gases, speak- 
 ing generally, expand to the same extent through equal ranges 
 of heat; provided all are subject to the same conditions. 
 
 These researches upon the rate of expansion of gases nat- 
 urally led me to investigate that of vapors; but expecting, from 
 the result of the above determinations, that they would expand 
 like gases, 1 decided to experiment upon only one vapor, and 
 chose that of sulphuric ether as being very easy to work with. 
 
 In order then to determine the rate of expansion of ether vapor 
 I made use of the two tubes of which I have already spoken, 
 atmospheric air serving throughout as a means of comparison. 
 This apparatus having been kept for some time in a heater 
 whose temperature was about 60, I admitted ether vapor into 
 one of the tubes and, atmospheric air into the other, in such a 
 way that each was filled to the same point. I then raised the 
 temperature of the heater from 60 to 100, and had the satis- 
 faction of seeing that, whether rising or falling, the ether va- 
 por and the atmospheric air always stood at the same division 
 at the same moment. This experiment, which Citizen Berth- 
 ollet has witnessed, was repeated many times and I have never 
 been able to note any difference in its rate of expansion as com- 
 pared with that of atmospheric air. I would however empha- 
 size the fact that a few degrees above the boiling point of ether, 
 its contraction was a little more rapid than that of atmospheric 
 air. This phenomenon goes with one which many substances 
 exhibit in passing from the liquid to the solid state, but which 
 is no longer noticeable a few degrees above that at which the 
 change is made. 
 
 This experiment, by showing that ether vapor and gases ex- 
 pand at the same rate, makes it evident that this property is in 
 no way dependent upon the peculiar nature of the gases and 
 the vapors but solely upon their elastic character, and conse- 
 quently leads us to the conclusion that all gases and all vapors 
 expand to the same extent for the same degrees of heat. 
 
 Since all gases are expanded to the same extent by heat and 
 are equally compressible, and since these two properties are 
 mutually dependent, as I shall show elsewhere, vapors which 
 are expansible to the same degree as gases must also be 
 equally compressible: yet I emphasize the fact that this latter 
 
 47 
 
MEMOIRS ON 
 
 conclusion can be true only so long as the compressed vapor re- 
 mains completely in its elastic state, and this demands that its 
 temperature shall be high enough to overcome the pressure 
 which would tend to make it assume the liquid state. 
 
 I have quoted Saussure and my experiments confirm his 
 view to the effect that very dry air and air holding in solution 
 more or less moisture expand at the same rate; I am therefore 
 in a position to draw from all I have said the following con- 
 clusions: 
 
 I. All gases, whatever their density or the quantity of water 
 which they hold in solution, and all vapors expand to the same 
 extent for the same degree of heat. 
 
 II. In the case of the permanent gases, the increase of vol- 
 ume which each of them suffers between the degree of melting 
 ice and that of boiling water, amounts to ^-5-5 of the original 
 volume, for a thermometer divided in 80 parts, or ^^.^ f tne 
 same volume, for a centigrade thermometer. 
 
 In order to complete this research, it remains for me to de- 
 termine the law of the expansion of gases and vapors, with the 
 object of finding. with its aid the coefficient of expansion for 
 any given degree of heat, and of establishing the true move- 
 ment of the thermometer. I am at work upon this new re- 
 search and, as soon as it is concluded, I shall have the honor of 
 laying an account of it before the Institute. 
 
 BIOGRAPHICAL SKETCH. 
 
 Louis JOSEPH GAY-LUSSAC was born in 1778. He received 
 his scientific education at the Ecole Polytechnique and the 
 Ecole des Fonts et Chausse'es, and in 1800 became assistant to 
 Berthollet. The research upon the expansion of gases by heat 
 was one of his first. Like his contemporary, Dalton, he was 
 much interested in the study of the atmosphere and in 1804 
 made analyses of the air, securing specimens from various 
 places one, at a height of over 6,000 meters, in a balloon 
 ascent. The analysis of water was also made at this time. In 
 1807 he published papers upon terrestrial magnetism and the 
 
 48 
 
EXPANSION OF GASES 
 
 results of his classic investigation of the volume-relations of 
 gases undergoing chemical change. Along with Thenard, he 
 studied the properties of the metals of the alkalies and of 
 chlorine, advocating, with Davy, their elementary character. 
 In 1809 he became Professor of Physics in the Faculte des Sci- 
 ences and Professor of Chemistry in the Ecole Polytechniqne; 
 in the same year, working with Thenard, he was able to isolate 
 boron and, later, iodine. The latter is considered one of his 
 most brilliant investigations. During the next few years he 
 published important memoirs upon the relationships existing be- 
 tween ethylene, alcohol and ether. In 1815 he discovered cyan- 
 ogen and prepared pure hydrocyanic acid. In 1815 he devised 
 the syphon barometer. 
 
 Gay-Lussac's ingenuity frequently made itself evident in the 
 construction of new forms of apparatus: in addition to the 
 syphon barometer, we owe to him a large number of useful in- 
 struments constantly employed in the laboratory. His death 
 occurred in 1850. 
 
 49 
 
THE DETERMINATION OF THE RATE OF 
 EXPANSION OF GASES BY HEAT. 
 
 BY J. B. BIOT. 
 
 Translated from Volume I, Chapter IX, of the Author's " Traite 
 de Physique" 
 
 51 
 
CONTENTS. 
 
 PAGE. 
 
 Third Method of Gay-Lussac: Apparatus ... 53 
 
 Need of excluding moisture; method of drying apparatus 54 
 
 Manipulation . . 55 
 
 Coefficient of expansion of glass containing -vessel . . 56 
 
 Results and conclusions 59 
 
EXTRACT FROM BIOT'S TREATISE ON 
 PHYSICS : 
 
 BEING CHAPTER IX OF VOLUME I. 
 
 The Determination of the Rate of Expansion of Gases by Heat. 
 
 THE experiments of MM. Lavoisier and Laplace upon the 
 expansion of solid substances have shown us that between the 
 limits of [the temperature of] melting ice and [that of] boil- 
 ing water, the expansion of solid metals is practically propor- 
 tional to that of mercury. The same relation, between these 
 limits, exists as well between the expansion of mercury and 
 that of dry gases. This important deduction has been com- 
 pletely established by the experiments which M. Gay-Lussac 
 has made with this object in view, upon the rate of expansion 
 of gases. This skilful physicist having been willing to make ' 
 known to me the details of his experiments, and to permit me 
 to sketch the apparatus which he has devised for the purpose, 
 I shall proceed to describe here the course which he followed 
 in his investigations and the results to which he was led. 
 
 In order to measure with accuracy the rate of expansion of 
 gaseous substances, it is necessary, first of all, to introduce 
 them, in known quantity, into tubes accurately graduated into 
 divisions of equal volume, and terminating in a bulb whose 
 volume should be considerable as compared with that of the 
 tube. It is necessary, further, that they should be kept there 
 under a known pressure, exposed to different temperatures and 
 the amounts by which they expand or contract under the dif- 
 ferent conditions observed ; in a word, it is necessary to make 
 a veritable gas thermometer. Yet although the statement of 
 this operation may be very simple, it demands, in order to be 
 accurate, many essential precautions which we shall now 
 discuss. 
 
 The first is, that the tubes in which the gases are contained 
 must be perfectly dry ; for we have already stated that glass 
 
 53 
 
MEMOIRS ON 
 
 tubes lying open and exposed to the atmosphere, become cov- 
 ered inside with a slight, imperceptible layer of water which 
 heat sets free by converting it into vapor. If one did not begin 
 by removing this thin layer of water, the vapor which it gives 
 off at different temperatures would mix with the gas introduced 
 into the tube and would increase its volume ; and, since the 
 amount of the vapor thus produced would increase with the 
 temperature until the slight layer of water had become com- 
 pletely removed, it is evident that this outside cause will con- 
 stantly increase the expansion proper of the gas, in proportion 
 as the temperature rises : such is the error into which many 
 physicists have fallen. 
 
 The only way to avoid this difficulty is to drive out this 
 slight film of moisture by heating the tube until it is changed 
 to vapor ; but in order that the air may not enter again, it is 
 necessary to fill the tube with mercury, which is made to boil 
 
 T T 
 
 FIG. 1. 
 
 there, as in a thermometer ; and which is important to notice 
 whether this boiling removes or not the whole of the film 
 adhering to the glass, at least it can no more give off vapor 
 when the tube is kept at any temperature less than that at 
 which mercury boils. This is the first precaution M. Gay-Lus- 
 sac has taken. 
 
 Next, in order to introduce only air or dry gases into the 
 tube, he connects to its open end another, larger tube TT y 
 Fig. 66 [Fig. 1], which may be regarded as a kind of receiver 
 intended to hold the gas. This tube is partly filled with bits 
 of muriate of lime [i. e., calcium chloride] or of any other salts 
 capable of absorbing moisture. It is even possible to produce 
 a vacuum in it in order to introduce the gas without admixture 
 of air. Then in order to let a definite quantity enter the tube, 
 M. Gay-Lussac makes use of a very fine iron wire previously 
 introduced into the bore. He inclines the tube or turns it up- 
 side down, and thus removes a large part of the mercury which 
 it contains, whose place is taken by a definite volume of gas 
 represented by GG, Fig. 67, [Fig. 2]. With care, it can be ar- 
 ranged to have only a short column of mercury M which acts 
 
 54 
 
EXPANSION OF GASES 
 
 as a piston, and all the space GG, from this point to the bulb 
 of the tube is filled with the dry gas which has been intro- 
 duced. If he is employing atmospheric air, there is no need of 
 producing a vacuum in the receiver TT; the air should be 
 allowed to remain some time in contact with the salts, after 
 which it is introduced into the tube GT, as we have described. 
 
 FIG. 2. 
 
 The gas having been introduced, it remains only to try the 
 effect of various known temperatures successively upon it ; for 
 this M. Gay-Lussac made use of a metal vessel AB, Fig. 67 [Fig. 
 2] rectangular in shape, the bottom of which fits upon a fur- 
 nace of the same size. Water is put in this vessel and is heated 
 to different temperatures. A thermometer F } placed vertically 
 in this water and whose stem projects above the cover of the 
 vessel, serves to indicate its temperature approximately and to 
 show if it is necessary to increase or diminish the heat. 
 
 The tube TG, however, which contains the gas, must not be 
 put in the water in this position; for we have already shown 
 by experiment that the different horizontal layers of a liquid, 
 which is being heated from the bottom, are not at the same 
 degree of temperature. Thus, in order to know exactly that 
 [temperature] which is producing an effect upon the gas, the 
 tube which contains it must be fixed in a horizontal position, 
 as Fig, 67 [Fig. 2] shows it; then its temperature may be 
 accurately determined by an excellent thermometer tt placed 
 opposite it in the same layer and likewise fixed in a horizontal 
 position. 
 
 55 
 
MEMOIRS ON 
 
 But we have stated that the vessel was of metal; how then 
 observe through its walls the divisions of the thermometer it 
 and the movable point G of the graduated tube to which at 
 any moment the gas-volume extends ? The point G and the 
 stem t of the thermometer cannot be kept continually outside 
 the hot-water bath, for then these parts respectively, being no 
 longer at the temperature of the bath, would introduce an 
 error into the determination. Yet one can, without inconveni- 
 ence, draw out the tubes from time to time, during the short 
 interval required to observe them: this M. Gay-Lussac accom- 
 plished in a very simple way. The openings 00' through which 
 the tubes pass into the vessel are closed with corks pierced 
 along their axes with a hole through which the tube in either 
 case can slip with some friction. Is it desired to observe the 
 condition of the gas GG? The tube TG is drawn out until 
 the end J/of the short column of mercury comes into sight at 
 the opening 0. It can then be seen at what division of the 
 tube it stands, and the volume of the gas at this moment is 
 known. Is it desired to note the temperature at the same 
 time? The stem is similarly drawn out until the end t of the 
 mercury column appears at the opening 0', and then the divi- 
 sion of the thermometer to which this corresponds indicates 
 the temperature at the time of the horizontal layer in which 
 the gas has been placed. 
 
 Thus at each moment the temperature of the gas is known 
 in the most exact way. Putting water at at first, therefore, 
 in the vessel, then raising the temperature by successive steps 
 to that of boiling; or, vice versa, returning from boiling to the 
 melting point of ice; the movement of the gas and that of the 
 thermometer can be compared with accuracy that is to say, at 
 any time, by the divisions marked upon the tube, the apparent 
 volume of the mercury and the apparent volume of the gas 
 may be known; but to have the real volumes, it is still necessary 
 to take into account the expansion of the glass of which the 
 tubes are made. 
 
 To study this effect properly, let us start from some definite 
 temperature for example, that of melting ice. Let us desig- 
 nate by F the number of divisions which the gas then occu- 
 pies in the glass vessel that encloses it, and let us make use of 
 
 56 
 
EXPANSION OP GASES 
 
 this number to express its volume. On the temperature rising 
 t degrees, the volume of the gas will increase and become 
 F(l-hf), designating by Jits cubical expansion from to t 
 degrees, and this is the unknown quantity we are looking for. 
 Let F be the number of divisions it now occupies in the tube. 
 As the latter expands each of its divisions has in reality a differ- 
 ent value from that which it had at the initial temperature, 
 and if the cubical expansion of the material of the tube, for one 
 degree of the thermometer, is represented by K, V' divisions 
 at the temperature t will be equal to V (1+Kt) of the original 
 divisions. This will therefore be the actual expression of the 
 new volume of the gas stated in terms of the original divisions 
 that is to say, we shall have 
 
 F (!+*) F (1+JR), 
 from which we obtain 
 
 ._ V-V VKt 
 ~~V~ ~T~ 
 
 The first term, ~ , is the cubical expansion for a volume 
 
 equal to unity, assuming the vessel did not expand; and the 
 
 V'Kt 
 second term,^^-, is the correction which must be made in the 
 
 first result on account of the expansion of the vessel. 
 
 F is determined at the beginning of the experiment; it is 
 the number of divisions occupied by the gas at the initial 
 temperature; subsequently, at other temperatures, the reading 
 gives F', the number of divisions the gas occupies at any given 
 moment. Moreover K is found from the expansion of solids; 
 thus the whole second number of our equation is known and, 
 consequently, on substituting their values for F, F, K, t, the 
 expansion 6 is found just as it would have been determined in 
 a vessel upon which [a change of] temperature produced no 
 effect. 
 
 It only remains to take account of the pressure to which 
 the gas is subjected, for we have seen that the volumes which 
 a given gas will occupy, at a given temperature, are inversely 
 proportional to the pressures to which it is subjected. Here, dur- 
 ing the experiments, the receiver, TT, Fig. 67 [Fig. 2] remains 
 always open; the pressure of the atmosphere thus acts freely 
 upon the short column of mercury, M 9 close to the gas GG. 
 E 57 
 
MEMOIRS ON 
 
 If the tube TG were vertical or inclined to the horizon, the 
 weight of this short column M would also act upon the gas; 
 but the tube being horizontal, this weight is entirely carried by 
 the glass tube. The short column M opposes no pressure, no 
 resistance to the motion of the gas unless, perhaps, that re- 
 sulting from its friction against the inner walls of the glass 
 tube; and this force is so small, when the column is short, that 
 it may be neglected. The weight, then, of the atmosphere is 
 the only force which weighs upon the gas GG, and it is deter- 
 mined by observing the height of the barometer at the time 
 of taking the readings. If this pressure remains constant 
 throughout the experiment, the corresponding volumes of gas 
 and of mercury may be directly compared with one another; 
 but, if it varies, all the readings must be reduced to one pres- 
 sure which is easy, making use of Mariotte's Law. 
 
 Thus, let p be the atmospheric pressure observed at the 
 beginning of the experiment and at the initial temperature, 
 when the gas in the vessel occupies a number Fof divisions. 
 Let us suppose that it is desired to reduce this volume to what it 
 would have been under the constant pressure of 0.76 m., to which 
 we refer all observations. Then, according to Mariotte's Law, 
 the volume Fmust be reduced inversely as tke pressures ; that 
 
 is to say, in place of Fwe have ^~. 
 
 In the same way, if we assume the pressure of the atmos- 
 phere to bey, when the gas is at the temperature t, and that 
 it occupies in the vessel a number of divisions represented by 
 F, this number, under a pressure of 0.76 m., but at a tem- 
 
 perature t, will become 
 
 . 
 
 Therefore to arrive at the expansions which would have re- 
 sulted if the pressure had remained constant and equal to 0.76, 
 
 V n V n' 
 
 we must substitute for Fand F in our formula, and -; 
 then the value of <5 becomes 
 
 . p f V'-p V p' 
 ' 
 
 P V ' P V 
 
 Use must be made of this formula in order to take account 
 of all the attending conditions. When the pressure is coh- 
 
 58 
 
EXPANSION OF GASES 
 
 sfcant throughout the experiment, we have p = p', and we fall 
 back upon the formula which we had found at first. 
 
 When d shall have been thus determined for an interval of t 
 degrees, the experiment is begun again or is continued for an 
 
 interval %t, 3t, ; and by comparison of the values of 6 with 
 
 one another, it may be known whether the rate of expansion 
 is uniform or variable. For, if it is uniform, the successive 
 expansions, 6, 2<f, 3<*, , will be proportional to the differ- 
 ences in temperature ; but if the rate of expansion is increas- 
 ing or decreasing, this proportionality will not obtain. Per- 
 forming the experiment in this way, with all the precautions 
 we have described, repeating it a great number of times, as 
 well with atmospheric air as with the different gases, M. Gay- 
 Lussac arrived at the following results : 
 
 All the permanent gases, subjected to equal [changes of] 
 temperature, under the same pressure, expand by exactly the 
 same amount. 
 
 The amount of their common expansion, from the tem- 
 perature of melting ice up to that of 100 degrees of the 
 centigrade thermometer, is equal to 0.375 of their original 
 volume at 0, assuming pressure to be constant. 
 
 Between these two limits the expansion of a gas is exactly 
 proportional to the expansion of mercury ; whence it follows 
 that, for every degree of the centigrade thermometer, and 
 under a given pressure, all gases expand by an amount equal to 
 0.00375 of the volume which they occupy at the temperature 
 of melting ice. 
 
 These results had been obtained almost simultaneously by 
 Mr. Dalton, the brilliant physicist of Manchester ; but the 
 work of M. Gay-Lussac was completed in France before that of 
 the English physicist could have been known. Mr. Dalfcon 
 finds the actual expansion slightly different from that [found] by 
 M. Gay-Lussac. He makes it equal to 0.372, and finds that, for 
 a given expansion of mercury, that of atmospheric air is a little 
 less in proportion and that this difference increases as the 
 temperature rises. Yet however great the skill of this philos- 
 opher in experimental research, we believe that the result of 
 M. Gay-Lussac may be considered as still more accurate, as 
 much by reason of the endless precautions he has taken to 
 
 59 
 
MEMOIRS ON 
 
 obtain it, as because it agrees very well with all the other 
 physical determinations in which there is need to use the figure 
 for the absolute rate of expansion of gases. 
 
 It would not be>out of the way to note on the other hand 
 that the ratio 0.00375 is exactly the one that has been found 
 for atmospheric air by the distinguished astronomer Tobie 
 Mayer, who appears to have been as skilful in the art of 
 physical experiment as in that of making and coordinating 
 astronomical observations. M. Gay-Lussac has stated in his 
 memoir that our renowned physicist, M. Charles, had long 
 before discovered the equal rate of expansion of gases and had 
 made it apparent by an apparatus constructed for his splendid 
 museum; but he had made no attempt to measure accurately 
 the absolute rate of their expansion. Doubtless we have reason 
 to regret the many other results of observation and experiment 
 which M. Charles had intended for use only in his public 
 lectures and which have never been published. 
 
 M. Gay-Lussac is in the same way convinced that the gaseous 
 substances produced by the evaporation of liquids expand at 
 the same rate as gases, so long as they do not become con- 
 densed to liquid form. To prove this, he removed the drying- 
 salts from the receiver TT, introduced into the tube TG gases 
 which had not been dried and consequently were charged with 
 moisture which could there take the form of vapor : moisture 
 which the drying-salts would take up with increase of weight. 
 By this means the space GG becomes filled with a mixture of 
 gas and aqueous vapor ; and this mixture, raised to different 
 higher temperatures in succession, expands exactly as would an 
 equal volume of dry gas. But one must not look for the same 
 law on lowering the temperature below the point at which the 
 gas was introduced ; for we shall prove later on, that a definite 
 volume of gas at a given temperature can hold only a certain 
 limited amount of water in the form of vapor, whence it follows 
 that if it is thus saturated with aqueous vapor at a given degree 
 of the thermometer and the temperature is lowered, a portion 
 of this vapor will be condensed to the liquid state. That part 
 which becomes liquid, occupying a far smaller volume, will 
 decrease the total volume of gas, will diminish its tension and, 
 
 60 
 
EXPANSION OF GASES 
 
 as a result of this double effect, will cause an apparent variation 
 in the laws of expansion. 
 
 M. Gay-Lussac has in the same way studied the rate of ex- 
 pansion of ether vapor ; he finds it the same as that of gases, 
 which leads to the belief that the conclusion holds good for 
 all kinds of vapors, so long as they remain in the gaseous 
 state. 
 
 With the aid of the results we have just described, we can 
 answer with accuracy all physical questions which might be 
 asked concerning the volume of a given quantity of gas sub- 
 jected in turn to various pressures and to various temperatures. 
 
 61 
 
RESEARCHES UPON THE RATE OF EX- 
 PANSION OF GASES. 
 
 BY HENRI VICTOR KEGNAULT. 
 
 From the Annales de Chimie et de Physique, 3d Series, volume 
 4, pages 5 67 (1842). Translated into German, Poggendorff's 
 Annalen, volume 55, pages 391 414 and 557 584. Also con- 
 tained in somewhat altered form in the Memoir es de V Academie 
 des Sciences, volume 21, pages 15 120 (1847). 
 
 63 
 
CONTENTS. 
 
 PAGE 
 
 Discussion of Rudberg's researches . . . . 65 
 
 " Dalton's " . - . . . . 71 
 
 First Series of determinations : 
 
 Apparatus and manipulation . . . . 74 
 
 Calculation of results ...... 79 
 
 Sources of possible error 80 
 
 Results 81 
 
 Second Series of determinations : 
 
 Apparatus and manipulation .... 82 
 
 Calculation of results ...... 86 
 
 Results with the several bulbs .... 87 
 
 Third series of determinations Expansion with constant 
 
 volume, I : 
 
 Apparatus and manipulation . 89 
 
 Calculation of results 92 
 
 Results 93 
 
 Disadvantages of the method .... 95 
 
 Fourth Series of determinations : Expansion with constant 
 
 volume, II : 
 
 Apparatus and manipulation .... 96 
 
 Calculation of results . . . . . . 99 
 
 Use of 'apparatus at higher pressures . . 100 
 
 Attempt to use Gay- Lussacs method .... 101 
 
 Discussion of possible sources of error in results . . 103 
 
 (a] Expansion of glass 103 
 
 (I) Barometric readings 104 
 
 (c) Temperature determinations .... 106 
 
 Coefficient of Expansion of gases other than Air: 
 
 Method 107 
 
 Results 109 
 
 Sources of gases 110 
 
 Application of Fourth Method to Carbon dioxide . . 113 
 
 " " " Sulphurous acid gas . 113 
 
 Direct comparison of two gases by Fourth Method . . 116 
 
 Biographical Sketch 120 
 
 64 
 
RESEARCHES UPON THE RATE OF EXPAN- 
 SION OF GASES. 
 BY VICTOR KEGNAULT. 
 PART I. 
 
 Upon the Rate of Expansion of Atmospheric Air. 
 
 THERE is no numerical quantity in physics which has been 
 submitted to a greater number of experimental determinations 
 than the coefficient of expansion of air, and yet we cannot say 
 that up to the present time this coefficient is known with suf- 
 ficient accuracy. 
 
 The experiments of the older physicists gave such diverse 
 numbers that it was impossible to draw a satisfactory conclusion ; 
 most of the conditions which affect the phenomenon [of gas ex- 
 pansion] were entirely unknown. 
 
 The brilliant experiments of M. Gay-Lussac upon the rate of 
 expansion of gases seemed bound to put an end forever to the 
 uncertainty of physicists. M. Gay-Lussac showed by a great 
 many experiments that the coefficient of expansion between 
 and 100 was the same for all gases, and for vapors so long as 
 they are kept a little above their points of condensation, and 
 that its value was 0.375. This coefficient was adopted by all 
 physicists and used in computations, until within the last few 
 years a Swedish physicist, M. Eudberg, threw doubt upon its 
 accuracy. By a series of carefully conducted experiments Rud- 
 berg sought to show that the coefficient of M. Gay-Lussac was 
 too high and that its true value must be between 364 and 365. 
 
 As Rudberg's work has never appeared in France, it would 
 seem as well to give an abstract of it here. 
 
 Rudberg has published two memoirs upon the coefficient 
 of expansion of air. In the earlier (PoggendorfFs Annalen, 
 Volume XLI) he uses for its determination a species of air- 
 thermometer formed of a bulb of glass [capable of] enclosing 
 from 120 to 150 grams of mercury and fused to a capillary tube. 
 A beginning is made by filling this apparatus with dry air. 
 
 65 
 
MEMOIRS ON 
 
 For this purpose the open [end of the] capillary is inserted in 
 a tube filled with bits of calcium chloride. The bulb is 
 thoroughly heated with an alcohol lamp, then is allowed to 
 cool. After repeating this operation fifty or sixty times there 
 is nothing but dry air in the bulb. 
 
 At other times he placed the chloride-tube in communication 
 with an air-pump and produced a vacuum in it fifty or sixty 
 times in succession, allowing the air to return each time. 
 These two methods of drying were employed indifferently; 
 they never gave [results] that differed noticeably. 
 
 The bulb, full of dry air and always fitted with 
 its calcium-chloride tube, was placed in a vessel 
 AB in which water was boiling (Fig. I), of such 
 size that the bulb and capillary tube were com- 
 pletely surrounded by the vapor. After the water 
 had boiled for three quarters of an hour or an 
 hour, the calcium-chloride tube was removed and, 
 ten minutes later, the drawn-out point of the 
 tube was sealed with a flame, and at the same 
 time the height of the barometer was read. 
 
 The bulb was weighed upon a very delicate 
 balance ; it was then fixed in the apparatus [shown 
 The capillary tube passes through a hole in a metal 
 capsule abc fastened to the upright AB. The arm CD is 
 lowered until the point of the capillary tube dips deep enough 
 in the small mercury-bath EFGH. The point of the tube is 
 broken off and the mercury rises into the bulb. The latter is 
 surrounded with crushed ice placed in the capsule ale; the water 
 formed by the melting of the ice flows off through the little tube 
 /. The bulb is thus kept at for at least two hours, the ice 
 being renewed as fast as it melts. The end of the capillary 
 tube is then stopped by means of a little soft wax held in a small 
 iron spoon, and at the same time the height of the barometer 
 is recorded. 
 
 The snow is then removed and a measurement made of the 
 height of the raised [column of] mercury. Eudberg used for 
 this purpose the apparatus KML consisting of a vertical 
 standard supported by a tripod with levelling-screws. Up and 
 down this stem travels an arm Imo carrying a cylindrical ring gn 
 
 66 
 
 FIG. 1. 
 
 in] Fig. 2. 
 
EXPANSION OF GASES 
 
 whose lower edge is exactly horizontal. This ring is lowered 
 until its lower edge coincides with the level of the mercury in 
 the bulb. At the same time the screw-rod KS is lowered until 
 its point reaches the level surface of the mercury in the bath. 
 The apparatus KML is then removed and the distance from 
 the ring to the point is measured with the aid of a graduated 
 rule. 
 
 The bulb is weighed with the mercury which it contains, 
 after the little piece of wax has been removed. 
 
 The thermometer tube is bent by means of a lamp in such a 
 way that its open end can dip in a small dish full of mercury. 
 The whole apparatus is filled with mercury which is carefully 
 
 FIG. 2. 
 
 heated until it boils. After it has cooled down again, the 
 bulb and tube are covered with crushed ice so that they may 
 become completely filled with mercury at 0. The bulb is 
 then removed, care being taken to catch in a small capsule the 
 mercury which escapes on account of expansion, and placed in 
 the boiler, the mercury which flows out being caught in the 
 same little capsule. This mercury is carefully weighed, as is 
 also that which has remained in the bulb. We thus have the 
 total weight of mercury which filled the apparatus at 0, and 
 
 67 
 
MEMOIBS ON 
 
 all the data necessary for calculating the coefficient of expan- 
 sion of the glass. 1 
 
 The glass used for Kudberg's apparatus was a Swedish pot- 
 ash glass of Reymira make. Its coefficient of expansion be- 
 tween and 100 was found to be 0.002285 as a mean of 
 twenty-four experiments, the extreme figures of which are 
 0.002256 and 0.002321. 
 
 The first three experiments to determine the coefficient of 
 expansion of air were made without bringing the air to ; the 
 bulb was merely placed in a cylinder full of water whose tem- 
 perature was taken with a thermometer. The three experi- 
 ments gave the following numbers: 
 
 0.3633 
 
 0.3617 
 
 0.3623 
 
 Mean = 0.3624 
 
 Rudberg does not consider these experiments very accurate, 
 (1) because the temperature of the water surrounding the bulb 
 was never perfectly stationary, but varied to a noticeable ex- 
 tent during the experiment; (2) because the difference of tem- 
 perature was not 100 but only 90. The experiments made 
 with cooling of the air to 0, gave: 
 
 0.3643 
 
 0.3654 
 
 0.3644 
 
 0.3650 
 
 0.3653 
 
 0.3636 
 
 0.3651 
 
 0.3643 
 
 0.3645 
 
 Mean = 0.3646 
 
 These experiments were made under very diverse barometric 
 pressures ; in fact, the height of the barometer varied from 
 742.77 to 779.85. Consequently, the temperature to which the 
 air was heated varied from 99.89 to 100.73. The height of 
 
 f 1 Note by Translator. Kudberg's method and apparatus are similar, 
 in all essential points, to those of Dulong and Petit in their comparison 
 of the air thermometer and the mercury thermometer. See page 3.] 
 
 68 
 
EXPANSION OF GASES 
 
 the mercury column drawn up into the apparatus varied from 
 35 mm. to 166.5 mm. 
 
 Rudberg then discusses the causes which could introduce 
 constant errors in his results. He states that capillarity could 
 not produce a noticeable effect in his apparatus because it was 
 acting in a surface of mercury of about two-thirds of an inch 
 diameter. The friction of the mercury against the walls of the 
 capillary tube produced no effect: otherwise differences would 
 have been noticed among the experiments where the height [of 
 the column] of the mercury drawn up varied from 35 mm. to 
 166 mm. 
 
 Eudberg made, further, two experiments with large glass 
 tubes of -inch diameter and 8 inches length. These experi- 
 ments he did not consider as accurate as the earlier ones, since 
 he could not boil the mercury in this form of apparatus. 
 They gave the two figures 
 
 0.3646 
 0.3662 
 
 Mean = 0.3654 
 
 Two experiments made with air which had not been dried 
 gave 0.3840 and 0.3902, which gives an idea of the influence of 
 moisture upon the coefficient of expansion. The same appara- 
 tus, having been dried again with care and filled with dry gas, 
 gave 0.3652. 
 
 In his second memoir (Poggendorff's Annalen, Volume 
 XLIV), Rudberg gives a series of experiments made by means 
 of a special apparatus having for its object the determination 
 of the tension which a given quantity of dry air exhibits at 
 and at 100; this quantity always occupying the same volume, 
 allowance being made each time for the expansion of the glass. 
 
 This apparatus is represented in Fig. 3. It consists of a 
 cylinder AB filled with dry air and communicating with a 
 second tube dC by means of a capillary tube Bbd. The tube 
 dC is cemented into the cover of a box containing a leather 
 pouch filled with mercury, the volume of which can be re- 
 duced, as in the case of barometers, by means of the screw M. 
 A barometer-tube about 50 centimeters high is cemented into 
 
 69 
 
MEMOIRS ON 
 
 the same cover. By means of the screw the mercury is made 
 to rise in the tubes. Upon the vertical part of the tube Id a 
 very fine scratch is made at a. The mercury is forced up to 
 this mark by means of the screw, (1) when the reservoir A B is 
 cooled to by the aid of ice ; (2) when it is heated to 100. 
 
 FIG. 3. 
 
 The volume of the air thus remains the same at the two 
 temperatures, if the expansion of the glass be left out of ac- 
 count. In order to measure the heights of the mercury in the 
 two tubes, there is placed directly behind these tubes a brass 
 rule EPRND, graduated in millimeters, the divisions of which 
 on the lower portion, from a to b, have been extended enough 
 to pass behind both of the tubes at one time. The difference 
 in height between a and the meniscus of the mercury in ED 
 can thus be easily determined. 
 
 The reservoir AB was thoroughly dried before cementing 
 the tubes into the box. To this end, the lower portion of the 
 
 70 
 
EXPANSION OF GASES 
 
 tube dC was drawn out to a point and connected with a very 
 large tube filled with calcium chloride, which in turn was con- 
 nected with a pump. The air having been exhausted about 
 fifty times and replaced by dry air, the drawn-out tip is closed 
 by means of a lamp. The tube dC was fitted into the box 
 filled with dry mercury, and when this tube was firmly ce- 
 mented in place, its point was broken off below the surface of 
 the mercury. 
 
 The capillary depression at a was determined by a direct ex- 
 periment before the narrow tube Bbd had been fused to the 
 reservoir AB. This depression had been found to be 18.5 mm. 
 
 The calculation of the experiment is extremely simple. 
 When the air is cooled to 0, let 
 
 ff = the barometric pressure, 
 h' = the difference of level aa, 
 e = the capillary depression at ; 
 we then have for the tension of the air, H' + 7^' e. 
 
 When the air is heated to the temperature Tby means of [the 
 vapor of] boiling water, we have for its tension, H" + h" e. 
 Hence 
 
 Twelve experiments made according to this method gave the 
 following figures : 
 
 0.3640 0.3643 
 
 0.3648 0.3648 
 
 0.3641 0.3653 
 
 0.3648 0.3640 
 
 0.3640 0.3664 
 
 0.3656 0.3645 
 
 Mean =0.3645 7. 
 
 This mean is the same as that found by the former method ; 
 Rudberg concludes that the expansion of air from to 100 
 must be between 0.364 and 0.365. 
 
 Rudberg closes his second memoir with an important state- 
 ment which had already been made by Gilbert in 1803 (Gilbert's 
 Annalen, Volume XIV, page 267), but which has since been 
 completely forgotten, namely, that the experiments of Mr. 
 Dalton and M. Gay-Lussac which have been looked upon as 
 
 71 
 
MEMOIRS ON 
 
 having given almost identical results, on the contrary differ a 
 good deal. In fact, in Dalton's memoir 1 taken from the 
 Memoirs of the Manchester Society (Gilbert's Annalen, Vol- 
 ume XII, page 313), it is stated, " I found from many deter- 
 minations that 1000 parts of atmospheric air, under the ordin- 
 ary pressure of the atmosphere, expand between 55 F. and 
 212 F., so as to form a volume of 1321 ; which gives, after 
 adding 4 parts for the expansion of the glass, an expansion of 
 325 parts for a difference of temperature of 157 of the Fah- 
 renheit scale." 
 
 It is evident that the volume of air which is here regarded as 
 unity is that which the air had at 55 F. or 12.78 C. If on 
 the other hand we consider as unity the volume of the air at 
 , and if we denote by lOOa the expansion between and 100 , 
 the results of Dalton give : 
 
 1 + 12.78 a : 1 + 100 a : : 1000 : 1325 ; hence 
 100 a = 0.892. 
 
 This is therefore the real result of Dalton's experiments. 2 
 Dalton does not, however, seem to have been aware of the error 
 which had crept into his calculations, for he says in his "New 
 System of Chemical Philosophy " 8 : "The volume of the air, 
 according to the experiments of M. Gay-Lussac and my own, 
 being 1000 at 32 F., becomes 1376 at 212 F." * 
 
 1 See pages 20-21. 
 
 2 Note by Translator : The figure 0.3912, as given by Rudberg and by 
 Magnus, is more nearly correct than 0.392. 
 
 8 See page 22. 
 
 4 Note by Translator: If Dalton made use of the data given in his 
 memoir of 1801 (See p. 20-21) as a basis for the statement quoted by Reg- 
 nault above as the latter evidently assumes he was clearly in error. 
 It happens that the coefficient in accordance with which a volume of 
 1000 would become 1325 through a rise of temperature of 157 F., or 
 87.22 C.. that is, for the number of degrees lying between the lowest 
 temperature he employed, 55 F., or 12.78 C., and the boiling-point of 
 water is 0.00207 for each Fahrenheit, and 0.00373 for each Centigrade 
 degree. This coincides quite closely with that found by Gay-Lussac in 
 the case of gases when the volume atO C. is compared with that at 100 
 C. Yet it is clear that Dal ton's 0.00373 represents the fraction of its 
 volume at 12.78 C. by which the volume of a gas increases for each de- 
 gree between 12.78 and 100 C.; while Gay-Lussac' s 0.00375 represents 
 
 72 
 
EXPANSION OF GASES 
 
 Thus, according to the experiments of Rudberg, the coefficient 
 of expansion of air accepted for a long time by physicists is 
 much too high. Should the figure 0.3646, which is the mean 
 result of his experiments, be adopted now in physical compu- 
 tations? 
 
 It seemed to me that new experiments were called for to re- 
 move all doubts in this direction, and I have not hesitated to 
 devote myself to the work, feeling that the determinations 
 would be of service to science, even if they merely confirmed 
 the results obtained by the skillful Swedish physicist. 
 
 I have carried out my experiments by four different meth- 
 ods. 
 
 the fraction of its volume at C. by which the volume of a gas increases 
 for each degree between and 100 C. The two coefficients are not 
 " sensibly the same," because they do not represent the same thing. 
 The words in quotation-marks are from Preston's Theory of Heat (p. 190, 
 footnote) where the author, following Regnault, assumes that Dal ton cal- 
 culated his coefficient from the data of his memoir of 1801, but somehow 
 misunderstands Regnault' s method of calculating the coefficient, and 
 claims (incorrectly) that the French savant had overlooked the fact that 
 Dalton's lowest temperature was 12.78 C. and notO. Yet if we use 
 the coefficient 0.003 <~3 in the way Gay-Lussac used his 0.00375, Dalton's 
 1000 volumes at 12.78 would have been reduced to 954.5 at 0, and 
 would have expanded to 1312.4 at 100, instead of the 1325 which he re- 
 cords. If, on the other hand, we make use of the coefficient 0.00392 cal- 
 culated by Regnault, Dalton's 1000 volumes at 12.78 would have been 
 reduced to 952.3 at 0, and would have expanded to 325.6 at 100, 
 which is what actually was found. 
 
 It would appear, however, that neither Rudberg, Regnault nor Pres- 
 ton has carefully read Dalton's statement in his " New System," for in 
 it he says, " The volume at 32 is taken 1000, and at 212 , 1376, accord- 
 ing to Gay-Lussac's and my own experiments. As for the expansion at 
 intermediate degrees, Gen. Roy makes the temperature at midway of 
 total expansion, 116 old scale; from the results of my former experi- 
 ments (Manch. Mem. Yol. 5, Part 2, page 599) the temperature may be es- 
 timated at 119; but I had not then an opportunity of having air at 32 . 
 By my more recent experiments, I am convinced that dry air at 32 
 will expand the same quantity from that to 117 or 118 of common 
 scale, as from the last term to 212," etc. 
 
 A study of this passage apparently shows that, after the publication 
 of Gay-Lussac's memoir, Daltou repeated his experiments with greater 
 care, using the freezing point of water as his lowest temperature, and 
 
 F 73 
 
MEMOIKS ON 
 
 FIKST SERIES OF EXPERIMENTS. 
 
 The determination was made by a method similar to that 
 used by Kudberg in his earlier research, and which is in other 
 respects that by the aid of which Dulong and Petit made the 
 comparison of the mercury thermometer with the air thermom- 
 eter. I replaced Rud berg's small bulb, however, which held 
 but 150 to 200 grams of mercury, by cylindrical reservoirs of 25 
 to 30 mm. diameter and of about 110 mm. length, capable of 
 holding 800 to 1000 grams of mercury. I preferred the cylin- 
 drical to the spherical form, because the former does not pro- 
 duce the refraction effects of the latter, which are likely to in- 
 troduce considerable errors when the heights of the mercury 
 [columns] drawn up are read from a distance with the aid of a 
 glass. It also seemed advisable to me to increase the capacity 
 of the air reservoir. 
 
 The cylindrical reservoir AB (Fig. 4) ended in a capillary 
 tube A CD the bore of which varied in different cases between 
 mm. and 2 mm. The capillary tube was drawn out to a point 
 and its end was bent at a right angle. 
 
 This apparatus was fixed by means of a cork E in the cover 
 
 obtaining results confirming closely those of his French contemporary. 
 These later figures are thus the ones referred to in the first part of the 
 passage quoted above. The fact that l< more recent experiments" with 
 "dry air at 32 " were made by Dalton seems to have been entirely 
 overlooked by the authors referred to above. 
 
 Moreover, nowhere in his 1801 memoir does Dalton calculate the coef- 
 ficient of expansion between and 100 of the gases with which he 
 experimented. He does not appear to have considered the question of 
 their volume at 32 F. at all ; his whole attention was directed to their 
 behavior above 55 F. Yet Biot, in his Treatise on Physics, praises 
 Dalton' s skill as an experimenter and states that the latter found 
 the expansion of gases between and 100 to be 0.372. (See page 59.) 
 Biot must himself have calculated the figure 0.372 from Dalton's data 
 of 1801 for Dalton does not give it in either of the extracts quoted 
 above, or else it is based upon later and more accurate determinations 
 made by the English philosopher after the publication of the work of 
 Gay-Lussac. 
 
 It seems much more reasonable to suppose that Dalton actually ob- 
 tained results after 1801 justifying the claim he makes in his New 
 System and explaining the statement of Biot, than to suppose that both 
 Dalton and Biot were guilty of the same arithmetical blunder. 
 
 74 
 
EXPANSION OF GASES 
 
 KK' of a tin-plate vessel V in which water is boiled. The va- 
 por which is formed in the lower part of the vessel is obliged 
 to pass out by way of the annular space LL' which is for the 
 purpose of preventing its cooling by reason of the contact of 
 the outside air, before escaping by the lateral pipe M. At N 
 there is a small tubulure and, in the inner wall and directly oppo- 
 site, a small round hole 0. In the neck is fitted by means of a 
 cork a bent glass tube F which acts as a manometer, and one 
 of the open ends of which passes through the hole and is 
 thus in direct communication with the interior of the vessel V. 
 The other end is open to the air. The water column contained 
 
 FIG. 4. 
 
 in the two vertical arms shows, by the difference of level, 
 whether the pressure is the same inside and out. The reser- 
 voir AB and the capillary tube attached to it are thus com- 
 pletely surrounded by the vapor of boiling water. 
 
 When the water is boiling vigorously, the tip of the capillary 
 tube is connected by means of a rubber tube with a drying 
 apparatus. This consists of U-shaped tubes G, G' } each about 
 
 75 
 
MEMOIKS ON 
 
 a meter long and 20 mm. in diameter. These tubes are filled 
 with broken pumice stone moistened with concentrated sulphu- 
 ric acid ; they are connected with one another by rubber tubes, 
 and with a small hand pump P. By means of this pump a 
 vacuum is produced twenty-five or thirty times in the appara- 
 tus, and, eacli time, the air is allowed to enter again very 
 slowly by opening the taps in the proper way. The taps are 
 left wide open the last time so that the air in the reservoir is in 
 direct communication with the atmosphere. 
 
 The apparatus is left in this condition for from a half-hour 
 to an hour ; the drying apparatus is then disconnected. As it 
 
 is conceivable that the 
 pumice stone might by 
 chance become packed 
 somewhere in the tubes GG' 
 and the enclosed acid pro- 
 duce a continual obstruc- 
 tion to the entrance of the 
 air, and as in consequence 
 an excess of pressure would 
 be needed to force it into 
 the reservoir, I have always 
 taken care to disconnect 
 first the rubber tube a; 
 it is evident that in this 
 way, even if the air of the 
 reservoir is under a slightly 
 lower pressure than that 
 of the atmosphere, it will 
 still be dried air, that con- 
 tained between a and D, 
 which will enter the res- 
 ervoir and produce equilib- 
 rium. In my experiments 
 this precaution was unneces- 
 sary, as the pumice stone was only soaked in sulphuric acid. 
 The rubber tube D is then removed and the apparatus allowed 
 to stand several minutes in direct communication with the 
 atmosphere ; finally the drawn-out tip of the capillary tube is 
 
 76 
 
 FIG. 5. 
 
EXPANSION OF GASES 
 
 closed by means of a blowpipe, and at the same time the height 
 of the barometer is recorded. We thus have the reservoir AB 
 filled with dry air at the temperature of the [water-] vapor and 
 under the pressure of the atmosphere. 
 
 The reservoir after being removed from the heater was 
 fastened in the support shown in perspective in Fig. 5. This 
 support consists of a circular plate EE' in the centre of which 
 is a short tube 0, and supported upon three vertical legs P, P', 
 P", joined for greater steadiness at their lower ends by a circle 
 of metal QQ'. Three inclined metal rods are arranged sym- 
 metrically about the short tube 0; they terminate above in 
 small balls with screw adjustment. The air reservoir AB rests 
 upon these balls and the capillary stem is held by a cork fitted 
 into the short tube. Greater steadiness is given it by means of 
 the screw V working in the movable cross-bar MN. 
 
 Upon one of the vertical legs P' is mounted a cross-bar mn 
 which carries a movable piece shown on a 
 larger scale in Fig. 6. It consists of a little 
 iron spoon JT attached to an iron stem fg 
 which can be raised or lowered at will in the 
 piece abed. This piece can be slid along 
 the horizontal ami mn, which in turn can 
 be fastened at any height to the leg P' by 
 means of the set screw v. 
 
 Upon another leg P is arranged a horizon- 
 tal arm st which is capable of adjustment 
 and can be held by a set screw; it carries a 
 screw rod ending at top and bottom in a 
 rounded point. 
 
 The reservoir is fixed in the apparatus in such a way that the 
 bent portion CD of the capillary tube is pointed directly 
 towards the leg P', and a mark is made upon the leg P> at the 
 height at which the adjustable piece mn must be fastened in 
 order that the centre of the little spoon K shall be exactly at 
 the height and in the direction of the bent portion of CD. 
 
 This being arranged, the apparatus is placed above a small 
 bath of mercury, in such a way that the capillary tube dips in 
 the mercury at least 5-6 centimeters. A very fine file mark 
 has been previously made across the stem CD at the point 
 
 77 
 
 FIG. 6. 
 
MEMOIRS ON 
 
 where it is desired to break it off. The tip is then broken off 
 with a small pair of pincers; the mercury enters the capillary 
 tube and rises to a certain height in the reservoir; this is then 
 surrounded with snow or finely crushed ice, and the apparatus 
 is allowed to stand undisturbed for at least an hour or an hour 
 and a half, in order to let it come exactly to the temperature of 
 melting ice. Meantime the spoon has been carefully lowered 
 to the proper depth in the mercury. From time to time the 
 apparatus is gently jarred to overcome the resistance should 
 there be any which the mercury might meet with in its ascent 
 within the capillary tube. 
 
 The little spoon is then pushed forward along its arm until 
 the opening of the capillary tube is buried in the wax, and at 
 the same time the exact height of the barometer is recorded. 
 The arm st is lowered along the leg P, and the point of the 
 screw is accurately adjusted to the level of the mercury surface 
 in the bath. The ice which enveloped the tube is completely 
 removed, and the drawn-up column of mercury is allowed to 
 come to the temperature of the surrounding air. 
 
 It now remains to measure the height of the drawn-up mer- 
 cury ; for this, I made use of a cathetometer of M. Gambey's 
 design, which gives directly, with its vernier, a reading within 
 a fiftieth of a millimeter. One sights with the horizontal tele- 
 scope at the level of the mercury 1 in the tube AB, then the 
 glass is lowered and is sighted at the upper point of the screw; 
 adding to the difference of level thus found the distance be- 
 tween the two points of the screw which has been previously 
 measured with the same instrument one has the total height 
 of the drawn-up mercury. More commonly we sight directly 
 at the lower point of the screw, after having lowered the bath 
 T which is easily done by removing the support 8. 
 
 The reservoir AB with the mercury drawn up is then re- 
 moved. It is weighed, then completely filled with mercury 
 
 1 Care must be taken, when one sights with the glass at the upper 
 line of the meniscus, not to be led into error through reflection-phe- 
 nomena at the curved surface of the mercury. The procedure which 
 seems to me surest, consists in placing a candle in the line of the menis- 
 cus and behind it, in such a way that the shape of the meniscus is out- 
 lined in black against the flame of the candle. 
 
 78 
 
EXPANSION OF GASES 
 
 which is thoroughly boiled to drive out air and moisture en- 
 tirely; finally it is buried in ice while the open end dips in a 
 dish full of mercury. After an hour and a half or two hours, 
 when one is certain that the mercury is perfectly stationary at 
 the opening in the tip, the ice is removed and the mercury 
 which flows out of the apparatus through expansion is caught 
 in a small capsule. The reservoir is next hung in the same 
 boiler which was used to expand the air ; the mercury which 
 escapes is caught in the little capsule. The barometer is read 
 while the boiling is in progress. The mercury caught in the 
 capsule is weighed, as well as the reservoir with the mercury 
 it still contains. The weight of the mercury at which 
 exactly fills the reservoir at is consequently known, and 
 one has given all that is necessary for calculating (1) the expan- 
 sion of the containing vessel; (2) the expansion of the air con- 
 tained. 
 
 Let H be the barometric pressure at the time when the 
 drawn-out tip of the tube was sealed with the blowpipe ; 
 
 TtliQ boiling point of water under this pressure; 
 
 ff" the barometric pressure when the tip was closed with the 
 wax under the mercury ; 
 
 h the height of the drawn-up mercury ; 
 
 P the weight of the mercury drawn up ; 
 
 P' the weight of the mercury at which fills the apparatus 
 at 0; 
 
 p the weight of the mercury forced out by expansion between 
 the temperature of melting ice and that (Ti) of water boiling 
 under a barometric pressure H\ ; 
 
 100 6 the amount, finally, by which a volume 1 of glass ex- 
 pands between and 100; 
 
 And 100 a the amount by which a volume 1 of dry air expands 
 between the same limits. 
 
 The heights H, H', h, are supposed, for greater simplicity, 
 to have been reduced to by calculation. We shall have for 
 determining 3 the equation: 
 
MEMOIKS ON 
 whence 
 
 (P'-p) l+_- 
 5550 J 
 
 PT 
 
 and for calculating a, 
 
 (P/ - P) (1 + a T) ~ = P' (1 + 6 T), 
 
 whence 
 
 In making my experiments in the way that has been de- 
 scribed I have not been slow to see a very serious source of 
 error. In breaking off the point of the capillary tube under 
 the mercury, I noticed that even when the stem dipped almost 
 a decimeter into the mercury, there was always a minute quan- 
 tity of air drawn in which added itself to the air in the reser- 
 voir. The mercury does not wet the glass, and there is a little 
 space, probably filled with air, between the glass tube and the 
 mercury. It is by way of this sheath that the outside air is 
 drawn in, by a process similar to that of a bugle, during the 
 ascending movement of the mercury. This phenomenon of 
 aspiration is sometimes noticed by the fact that whole bubbles 
 of air rise in the capillary tube after the manner of a piston. 
 
 I had much difficulty at first in preventing this result. By 
 placing upon the part of the tube under the mercury many 
 small discs of a substance wetted by mercury, like well cleaned 
 brass, I succeeded in preventing the entrance of the outside air. 
 In order to be completely out of reach of this source of error, 
 I combined this method with another which consists in pour- 
 ing upon the mercury, before breaking off the point and after 
 having taken hold of the tip with the pincers, a layer of con- 
 centrated sulphuric acid. This layer of acid is removed when 
 the reservoir has been lowered to by the ice ; the surface of 
 the bath of mercury is cleaned and then the arm Kn is lowered. 
 
 It is also important that the iron pincers with which the 
 point of the capillary tube is broken off, should always be at 
 some distance from the scratch of the file upon the stem by 
 which the break is brought about. Otherwise, if the opening 
 of the capillary tube touches the pincers, one may see rise in 
 
 80 
 
EXPANSION OF GASES 
 
 the tube a little bubble of air which has its source in that which 
 remains adhering to the surface of the pincers. 
 
 I bring together in the following table the results obtained 
 in the fourteen experiments I made by this method. 
 
 Number 
 of 
 Experi- 
 ment 
 
 II 
 
 , 
 
 h 
 
 P 
 
 ff 
 
 T 
 
 Hi 
 
 ft 
 
 P 
 
 1005 
 
 1+100 a 
 
 
 
 ram. 
 
 mm. 
 
 mm. 
 
 gr. 
 
 gr. 
 
 
 
 mm. 
 
 
 
 gr. 
 
 
 
 
 1 
 
 760.03 
 
 760.57 
 
 111.02 
 
 856.145 
 
 119.915 
 
 100.00 
 
 760.60 
 
 100.02 
 
 12.870 
 
 0.002714 
 
 1.36556 
 
 
 2 
 
 759.67 
 
 755.72 
 
 98.67 
 
 770.465 
 
 116.780 
 
 99.99 
 
 753.75 
 
 99.7V 
 
 11.665 
 
 0.002576 
 
 1.36626 
 
 
 3 
 
 750.40 
 
 749.81 
 
 99.82 
 
 805.75 
 
 12260 
 
 99.64 
 
 " 
 
 ' 
 
 " 
 
 0.002650 
 
 1.36659 
 
 
 4 
 
 744.61 
 
 744.78 
 
 100.60 
 
 800.27 
 
 120.19 
 
 99.43 
 
 744.60 
 
 99.43 
 
 12.050 
 
 0.002601 
 
 1.36579 
 
 
 5 
 
 747.99 
 
 748.79 
 
 106.35 
 
 790.69 
 
 114.31 
 
 99.55 
 
 748.20 
 
 99.56 
 
 11.931 
 
 0002592 
 
 1.36625 
 
 
 6 
 
 751.48 
 
 752.68 
 
 102 32 
 
 913.48 
 
 137.74 
 
 99.68 
 
 " 
 
 11 
 
 " 
 
 0.002680 
 
 1 .36549 
 
 
 7 
 
 763.27 
 
 763.27 
 
 97.45 
 
 855.24 
 
 136318 
 
 100.13 
 
 763.30 
 
 100.13 
 
 13.015 
 
 0.002544 
 
 1.36673 
 
 
 8 
 
 765.34 
 
 765.00 
 
 102.50 
 
 854.86 
 
 130.60 
 
 100.20 
 
 765.30 
 
 100.20 
 
 13 025 
 
 0.002537 
 
 1.36634 
 
 
 9 
 
 764.14 
 
 763.92 
 
 102.87 
 
 805.14 
 
 122.79 
 
 100.16 
 
 764.10 
 
 100.16 
 
 12.225 
 
 0.002583 
 
 1.36689 
 
 
 10 
 
 763.34 
 
 763.62 
 
 102.17 
 
 854.79 
 
 131.10 
 
 100.13 
 
 763.51 
 
 100.14 
 
 13.005 
 
 0.002548 
 
 1.36610 
 
 
 11 
 
 754.55 
 
 752.34 
 
 105.80 
 
 790.49 
 
 113.364 
 
 99.80 
 
 754.50 
 
 99.80 
 
 11.942 
 
 0.002607 
 
 1.36671 
 
 
 12 
 
 750.29 
 
 750.57 
 
 68.48 
 
 853.82 
 
 163.794 
 
 99.64 
 
 " 
 
 M 
 
 " 
 
 0.002570 
 
 1.36591 
 
 
 13 
 
 751.94 
 
 751.72 
 
 74.91 
 
 769.452 
 
 141.710 
 
 99.70 
 
 750.86 
 
 99.66 
 
 11.633 
 
 0.002576 
 
 1.36041 
 
 
 14 
 
 764.62 
 
 764.50 
 
 122.31 
 
 853.447 
 
 108.417 
 
 100.18 
 
 768.63 
 
 100.32 
 
 13.008 
 
 0.002551 
 
 1.36673 
 
 
 19.12776 
 
 Mean ^ . = 1.36623 
 
 Extremes. 
 
 .. Ji- 
 
 56689 
 !6549 
 
 ll.! 
 
 Greatest difference 0.00140 
 
 The mean for the fourteen experiments is 1.36623. The 
 
 difference between the two extreme figures 1.36689 
 
 and 1.36549 
 
 is .0.00140 
 
 that is, what amounts to, at most, TT5 V^ of the quantity to be 
 measured. 
 
 The figures given by the fourteen experiments are all much 
 higher than the mean 1.3646 which Rudberg obtained in the 
 experiments made by a quite similar method. I believe that 
 this difference can be ascribed to the fact of the sucking in, in 
 Rudberg's experiments, of the outside air ; it seems unlikely 
 that, working by his method, this source of error could have 
 been avoided : on the other hand it is clear that it escaped his 
 notice, if only because he does not mention it. 
 
 The errors introduced through this sucking-in are so much 
 the more noticeable as one works with a smaller volume of air. 
 
 I did not at first succeed in preventing this sucking-in ; I am 
 
 81 
 
MEMOIRS ON 
 
 convinced that in my earlier experiments it still had a notice- 
 able effect and rendered some of my figures too low. What con- 
 firms me in this view is that, starting from the time when the 
 sucking-in was, made impossible, I obtained no figure lower 
 than 1.3658. 
 
 SECOND SERIES OF EXPERIMENTS. 
 
 The experiments of this second series were made by a method 
 slightly different from that followed in the former series ; but 
 the apparatus was arranged so that the volume of air subjected 
 to experiment remained practically the same at the temperature 
 of melting ice and at that of boiling water, so that the whole 
 effect of the expansion by heat is changed to a variation of 
 tension. 
 
 A glass bulb of 350 to 400 cubic centimeters' capacity is 
 sealed to a capillary tube about 38 centimeters long ; on this 
 capillary tube, at a distance of 11 centimeters from the bulb, 
 is put a piece of very regular tubing about 50 mm. long and of 
 sufficiently great diameter to show only a very slight capillary 
 effect. The capillary tube at its end is drawn out to a point 
 and bent at a right angle. 
 
 The first thing to be done consists in calibrating this appara- 
 tus accurately and determining its coefficient of expansion. 
 For this it must be completely filled with mercury at the 
 temperature of 0. This is a delicate operation, as all physi- 
 cists will agree, for it is nothing else than constructing a 
 thermometer whose reservoir shall contain about 5 kilograms 
 of mercury. 
 
 To introduce the mercury, the bulb is connected, by means 
 of a rubber tube D, Fig. 7, with a bent tube DE fastened to a 
 support ; mercury is poured into this tube DE. If the bore 
 of the capillary tube is not very small, the bulb is easily filled 
 three-quarters full without any necessity for exhausting through 
 the tube E ; but to succeed in filling it, one may have to 
 exhaust several times by means of the tube E. The best way 
 is to connect this tube with the small pump of Fig. 4, page 75. 
 The bulb may thus be filled in a very short time. 
 
 It is then necessary to bring the mercury to boiling : to this 
 
EXPANSION OF GASES 
 
 end the bulb A is placed upon a hollow grating GG over a 
 small furnace F, Fig. 8, the capillary tube having an inclina- 
 tion of about 45 and its bent end CD being below the surface 
 in a dish full of very pure mercury. Some coals are then put 
 in the furnace, below the grating, then they are successively 
 placed upon the grating itself and upon the bulb, and finally 
 
 FIG. 7. 
 
 FIG. 8. 
 
 the latter is entirely covered with hot coals. When the mercury 
 in the bulb approaches the boiling temperature, the mercury in 
 the dish D is heated with an alcohol lamp, and with a second 
 alcohol lamp the capillary tube is cautiously heated throughout 
 its length. As soon as the mercury begins to boil in the bulb, 
 the operation must be watched with the greatest care ; for if this 
 boiling becomes too vigorous, if it drives out of the bulb too 
 large a volume of liquid mercury displaced by mercury vapor, 
 it is almost impossible to prevent the apparatus being broken 
 at the instant when, the boiling having stopped, the mercury 
 rushes back into the bulb ; this results in very violent hammer- 
 ing and return-shocks which ordinarily extend as far as the 
 bent part CD of the capillary tube. 
 
 Therefore as one sees the mercury boiling in the vessel, a 
 part of the coals must quickly be removed and the operation 
 be made as smooth as possible. The coals are taken away 
 entirely as soon as the moisture seems to have been completely 
 
 83 
 
ME MO IKS ON 
 
 driven out, or even when the volume of mercury vapor has 
 become considerable. The mercury then returns into the 
 apparatus and, as it has been previously heated in the dish, it 
 does not break the capillary tube, as it would certainly do with- 
 out this. When the bulb is once more full, one looks to see if 
 a trace of moisture remains ; in case some still remains, the 
 boiling must be begun again. Speaking generally, it serves 
 better to bring it to the boiling point again and again, rather 
 than to continue the boiling for too long a time ; in this way 
 the breaking of the apparatus is more easily avoided. 
 
 When the vessel is completely full of mercury, it is allowed 
 to cool to the temperature of the air, then is surrounded with 
 a thick envelope of crushed ice. It requires* many, hours for 
 the mass of mercury to arrive absolutely at the temperature of 
 0. When it is certain that this point has been reached, the 
 dish full of mercury is removed and is replaced by a small 
 empty capsule. The ice having been got out of the way, the bulb 
 is warmed with the aid of hot coals placed at some distance 
 from it, so as to raise it to a temperature some degrees higher 
 than the surrounding one; then it is hung in a small bag in 
 the boiling apparatus of Fig. 4 [page 75], to which an exten- 
 sion has been fitted, so that the whole capillary tube is sur- 
 rounded by the steam, and the mercury is caught in the same 
 capsule. By weighing the mercury forced out and that re- 
 maining in the apparatus, it is evident we have the necessary 
 data for calculating the volume of the apparatus at and 
 the extent to which it expands between and 100. 
 
 To find the expansion of air, the bulb is hung in the boiler 
 after the mercury has been so completely removed that not the 
 smallest globule remains upon the walls or in the tube. The 
 bulb is connected with the drying apparatus, Fig. 4. In a 
 word, one goes to work exactly as has been described in the 
 account of the former series. 
 
 When the end of the capillary tube has been sealed with a 
 lamp, the apparatus is adjusted to a support shown in Fig. 9. 
 The expanded part B of the tube comes below the plate EE' '. 
 By means of a cork on the stem at M, a tin-plate tray is put in 
 place, in which crushed ice must be piled up, to keep the vol- 
 ume B at 0. The capillary tube dips in a small bath of mer- 
 
 84 
 
EXPANSION OF GASES 
 
 cury T. The tip of the bent part CD is broken off, all the 
 precautions being exactly followed which have been pointed 
 out in the first account, to prevent the entrance of air; finally 
 the vessel A is surrounded with ice after having put over it 
 from above a cylinder of tin-plate which is entirely filled with 
 crushed ice. In the same way the volume B and the part of 
 the capillary stem which is above the tray M are surrounded 
 with ice. 
 
 Upon one of the legs of the support P is arranged a mov- 
 able arm mn carrying the small adjustable spoon of Fig. 6; 
 this is lowered into the mercury. A mark has previously been 
 
 FIG. 9. 
 
 made upon the leg P' at the point where mn should be clamped 
 in order that the spoon JTmay be at the level and in a line 
 with the tube CD. 
 
 The apparatus having been left in the ice for about an hour, 
 the tip D is sealed by pushing forward the spoon K, and at the 
 same time the barometer is read; finally, the point of the 
 screw #, which is arranged upon a small special apparatus E, 
 is made to coincide with the surface of the mercury in the 
 bath. 
 
 The ice which is in the tray M is then removed. At the 
 end of three-quarters of an hour or an hour, when it is certain 
 that the column of mercury drawn up is in temperature-equi- 
 
 85 
 
MEMOIRS ON 
 
 librium with the surrounding air, the height of this column is 
 measured with the cathetometer. The dimensions of the tube 
 and the level at which the mercury bath is placed, are such that 
 the mercury comes to rest in the space B and fills it about 
 half full. 
 
 The apparatus is detached and the mercury which has made 
 its way in is weighed. 
 
 The tubing of which the space B is made was chosen in suc- 
 cessive cases of different diameters; these dimensions were 
 never great enough for the capillarity to become nil, but the 
 capillary depression is determined each time, by direct experi- 
 ment, in that part of the tube where the surface of the mer- 
 cury comes to rest. For this purpose this tube is held vertical 
 with both ends open, and dipping in a bath of mercury. On 
 the slide which supports the glass of the cathetometer a hori- 
 zontal metallic rod is fastened, to the end of which is fixed a 
 vertical pointer whose tip is adjusted for contact, successively 
 with the top of the meniscus in the tube and with the mercury 
 surface in the bath. The distance traversed by the zero of 
 the vernier of the instrument is the capillary depression. 
 
 We then have all the data necessary for calculating the ex- 
 pansion of the air. Using the same letters to designate simi- 
 lar things, as in the former method and, in addition, repre- 
 senting by c the capillary depression in the space B, clearly we 
 have the equation 
 
 (1 + 6 T) H = (i ^VH' (h + c)] (1 + & T)\ 
 whence 
 
 l + aT = \H'-(h + c)} /VIH 
 
 Let us assume in all cases that the columns of mercury have 
 been reduced to by calculation. 
 
 Three different vessels, A, B, C, were used in these experi- 
 ments; to these were successively joined capillary tubes of 
 different bores. 
 
 I shall distinguish as many series of experiments as different 
 forms of apparatus. 
 
 86 
 
EXPANSION OF GASES 
 
 I. The results with this apparatus are as follows: 
 
 p = 4330.0 gr. 
 c = 1.10 mm. 
 
 The coefficient of expansion of the glass could not be deter- 
 mined as the apparatus was broken during the boiling of the 
 mercury. For this one experiment made with vessel A the as- 
 sumption is made that 100<5 = 0.002306, as was found by ex- 
 periment with the vessel B. 
 
 The experiment upon the expansion of air gave 
 
 . 4- 100 a 
 
 1.36629 
 
 II. This apparatus was made with the vessel B; we have: 
 
 p=4274.34gr., 
 p = 65.708, 
 c= 1.10mm., 
 // = 749.37, whence Tl = 99.60 . 
 
 We deduce from this 
 
 100^ = 0.002306. 
 
 H 
 
 H' 
 
 h -f- c 
 
 P' 
 
 T 
 
 mm. 
 739.61 
 
 mm. 
 
 739.86 
 
 mm. 
 194.38 
 
 gr. 
 14,233 
 
 99.23 
 
 
 H 
 
 H' 
 
 2 
 3 
 
 mm. 
 739.24 
 758.64 
 
 mm. 
 739.21 
 758.53 
 
 mm. 
 
 193.58 
 199.51 
 
 P' 
 
 gr. 
 
 17,735 
 17,335 
 
 T |14-100a 
 
 99.22 
 99.95 
 
 1.36645 
 1.36593 
 
 III. Apparatus made with the vessel B, but using for the 
 space B on the capillary tube, a tubing of much greater diame- 
 ter. 
 
 For this apparatus it was found 
 P =4306. 86 gr., 
 p = 66.68, 
 c = 0.22 mm., 
 Hi= 769.04, hence T\ = 100.34 ; 
 from which we find 
 
 100 6 = 0.002302. 
 With this apparatus I obtained the following figures : 
 
 
 H 
 
 H' 
 
 h + c 
 
 P' 
 
 T 
 
 1 + 100 a 
 
 
 mm. 
 
 mm. 
 
 mm. 
 
 gr. 
 
 
 
 4 
 
 764.70 
 
 764.31 
 
 198.78 
 
 36.095 
 
 100.18 
 
 1 .36610 
 
 5 
 
 767.24 
 
 767.19 
 
 199.98 
 
 34.825 
 
 100.27 
 
 1.36585 
 
 6 
 
 768.10 
 
 767.40 
 
 199.62 
 
 34.845 
 
 100.30 
 
 1.36590 
 
 7 
 
 770.57 
 
 770.70 
 
 200.86 
 
 34.490 
 
 100.40 
 
 1.36615 
 
 8 
 
 771.07 
 
 770.26 
 
 199.53 
 
 41.780 
 
 100.41 
 
 1.36691 
 
 87 
 
MEMOIRS ON 
 
 IV. Apparatus made with the vessel C. 
 P = 4878.60 gr., 
 
 P = 
 c = 
 Hi = 
 From this we deduce 
 
 74.795, 
 
 0.54 mm., 
 
 749.32, hence Ti = 99.60. 
 100 6 = 0.002349. 
 
 
 II 
 
 JET 
 
 h + c 
 
 P' 
 
 T 
 
 1 + 100 a 
 
 
 mm. 
 
 mm. 
 
 mm. 
 
 gr. 
 
 
 
 9 
 
 748.13 
 
 745.89 
 
 193.04 
 
 32.42 
 
 99.56 
 
 1.36708 
 
 10 
 
 754.10 
 
 751.51 
 
 194.73 
 
 30.64 
 
 99.78 
 
 1.36695 
 
 11 
 
 740.14 
 
 744.53 
 
 196.86 
 
 32.305 
 
 99.26 
 
 1.36633 
 
 12 
 
 746.91 
 
 748. 13 
 
 196.23 
 
 31.355 
 
 99.51 
 
 1.36708 
 
 13 
 
 747.54 
 
 747.28 
 
 194.69 
 
 31.486 
 
 99.53 
 
 1.36650 
 
 V. Apparatus made with the bulb C, but using for the space 
 B a tubing of a greater diameter and for capillary tubing one 
 of finer bore. 
 
 For this apparatus we have : 
 
 P = 4923.60gr., 
 c = 0.22 mm. ; 
 we have assumed 100 6 = 0.002349. 
 
 
 H 
 
 H' 
 
 h + c 
 
 P' 
 
 T 
 
 1 +100 a 
 
 
 mm. 
 
 mm. 
 
 mm. 
 
 gr. 
 
 
 
 14 
 
 746.69 
 
 747.16 
 
 191.98 
 
 58.551 
 
 99.50 
 
 1.36615 
 
 15 
 
 751.97 
 
 750.18 
 
 191.50 
 
 56.69 
 
 99.70 
 
 1.36594 
 
 16 
 
 746.49 
 
 746.19 
 
 191.76 
 
 54.865 
 
 99.50 
 
 1.36660 
 
 17 
 
 752.50 
 
 751.45 
 
 192.17 
 
 61.30 
 
 99.72 
 
 1.36666 
 
 VI. Apparatus constructed with the same bulb, substituting 
 for the finer capillary tube another of a larger bore. 
 The data for this apparatus are the following : 
 P = 4926.4 gr., 
 c = 0.22 mm. ; 
 we have assumed 100 6 = 0.002349. 
 
 This apparatus was used for but one experiment upon atmos- 
 pheric air ; it was intended for some experiments upon other 
 
 18 
 
 H 
 mm. 
 
 758.24 
 
 H' 
 
 mm. 
 
 758.78 
 
 mm. 
 195.68 
 
 P 
 
 gr. 
 
 58.31 
 
 T 
 
 99.93 
 
 1 + 100 a 
 1.36614 
 
 Then bringing together all the figures obtained in this series 
 of experiments 
 
 88 
 
EXPANSION OF GASES 
 
 1.36629 
 1.36645 
 1.36593 
 1.36610 
 1.36585 
 1.36590 
 1.36615 
 1.36591 
 1.36708 
 
 1.36695 
 1.36633 
 1.36708 
 1.36650 
 1.36615 
 1.36594 
 1.36660 
 1.36666 
 1.36614 
 
 The mean of all these experiments is 
 
 1.36633. 
 
 It does not practically differ from that obtained in the former 
 series. 
 
 THIRD SERIES OF EXPERIMENTS. 
 
 This third series of experiments was made by means of an ap- 
 ]o f o 
 
 paratns copied from that described by Rudberg in his second 
 memoir and which is represented in Fig. 3 [page 70 ]. The ap- 
 paratus which I constructed is shown in Figs. 10, 11, 12. 
 G 89 
 
MEMOIES ON 
 
 A cylindrical glass reservoir AB, 35 millimeters in diameter 
 and 170 mm. long, is sealed to a capillary tube BCDE, twice 
 bent at right angles. This tube terminates in a piece of tubing 
 EE of much larger size, which dips iu a small mercury bath 
 MM'. 
 
 This bath consists of a cylinder of heavy glass whose two 
 edges are tightly pressed against the two cast mountings M, 
 M', by means of the screw rods t, t ', t". The upper casting has 
 two tubulures T, T', provided with screw threads on the outside. 
 These tubulures are closed by two copper screw caps bored 
 through the centre with holes to allow tubes to enter. The 
 lower casting carries a screw thread in which works a large 
 screw rod KL supporting a cast piston P inside the glass cylin- 
 der. This piston has a covering of linen greased with tallow : 
 at its centre is a small packing-box filled with oakum, through 
 which moves an iron rod//', 8 millimeters in diameter, which 
 screws up and down inside the large rod KL, and ends outside 
 with the knob/. 
 
 The small bath is fixed by means of set screws to a cast ver- 
 tical support NN' 9 but in such a way that it can be made to 
 move along the slots r r', which is convenient for adjusting 
 the tubes. This bath is otherwise completely filled with 
 thoroughly dry mercury. 
 
 We begin by determining by a preliminary experiment the 
 capacity of the cylindrical reservoir AB and its coefficient of 
 expansion. We determine in the same way the volume of the 
 capillary tube from C to E, as well as that of the small portion 
 of the larger tube E a down to a very fine mark scratched upon 
 this tube at a. We then dry the reservoir completely and fill 
 it with dry air : for this the drawn-out end of the tube is con- 
 nected with the drying apparatus, Fig. 4, page 75, and the whole 
 length of the reservoir and tube are warmed with hot coals. 
 A vacuum is produced a great many times and each time the 
 air is allowed to enter again. The hot coals are then removed, 
 there being free communication with the atmospheric air. 
 When the reservoir has cooled, it is placed in very cold water 
 or even in some ice ; finally, after some time, the tip of the 
 tube is closed by means of the blowpipe. 
 
 The cast upright NN' carries a cast bracket-arm FF ' F" 
 
 90 
 
EXPANSION OF GASES 
 
 fastened with screw bolts in the slots cut in the upright NN'; 
 it can thus be adjusted at various heights. To this bracket- 
 arm is fastened permanently the copper cover GG of a vessel 
 of the same metal GHH'G. The cover is provided with two 
 tubulures /, /' : in one the reservoir of air AB is fixed by means 
 of a cork ; in the other is placed a mercury weight-thermometer 
 A'B', of exactly the same shape and dimensions as the air 
 reservoir. The two tubes rest upon a small cross piece A A 
 fastened to the rod JJ'. 
 
 The tube EF is introduced into the tubulure I 7 and, in order 
 to fasten it hermetically, is wrapped with a strip of linen 
 greased with tallow, which is then forced by means of the screw 
 cap E into the annular space formed in the tubulure. We thus 
 obtain an air-tight connection which will resist very great pres- 
 sure. The point of the tube UF is then broken off by means 
 of an iron rod introduced through the second tubulure T', and 
 in this second tubulure is fastened, in exactly the same way, a 
 piece of barometer tubing 00', perfectly cylindrical through- 
 out its length and of exactly the same diameter as the end 
 tubing EF possesses below where it is drawn out. Besides it 
 was shown by direct experiment that there was no difference 
 between the capillary depressions in the two tubes. 
 
 To conduct the experiment, the two reservoirs AB, A B' are 
 surrounded with melting ice which is put in a small bag and 
 hung from the copper cover GG' . By turning the rod KL the 
 piston is forced up until the mercury comes to rest at a in the 
 tube EF; the fine adjustment is made with the aid of the thin 
 rod f. A determination of the difference of level is then made 
 with the cathetometer, and at the same time the barometric 
 pressure is recorded. 
 
 The ice and the bag which contains it are then removed, the 
 vessel GHH'G' is fastened by means of screws to its cover GG', 
 and the water which it contains is then raised to boiling. By 
 pushing up the piston the mercury is maintained at the level a 
 in the tube EF. When it is certain that the air has come to 
 the temperature of the vapor, the mercury level is adjusted 
 exactly at a by means of the rods KL andjf ', and the difference 
 of level of the two columns of mercury is read with the cathe- 
 tometer, as well as the height of the barometer. 
 
 91 
 
MEMOIRS ON 
 
 I made some experiments at first, taking, as Rudberg did, 
 the point a upon the capillary stem ; but I found that it was 
 very difficult by this method to get accurate results. Thus, 
 although in one experiment the tube was of more than 1 mm. 
 diameter, the movement of the mercury in the tube was very 
 irregular, by reason of the variation in the capillary action. 
 Sometimes the column in 00 would rise more than 1 mm., 
 without the mercury at a being displaced to a visible extent ; 
 in the same way, on lowering the piston, the column had often 
 fallen several millimeters in the tube 00', while the meniscus 
 at a had only become flattened ; this sluggishness was not 
 entirely overcome by even quite sharp taps given the appara- 
 tus. 
 
 It became necessary to take the point a upon the larger tubing 
 EF. As this tubing was of exactly the same diameter as the 
 barometer tubing there was no correction to introduce for cap- 
 illarity; but it was necessary to take account of the small vol- 
 ume of air which was not heated. 
 
 Let P be the weight of mercury at filling the reservoir AB 
 up to C when it is at 0; 
 
 p the weight of mercury which flows out at the temperature 
 of water boiling under the pressure H', or at the tempera- 
 ture T 1 -, 
 
 p' the weight of mercury which fills the capillary tube CDE 
 and the part Ea of the larger tubing EF; 
 
 H the barometric pressure at the time when the reading is 
 made, the reservoirs being kept at by melting ice; 
 
 h the difference of level of the two columns of mercury; 
 
 t the temperature of the surrounding air. 
 In the same way let us represent by 
 
 H' the barometric pressure when the reservoirs are heated by 
 boiling water; 
 
 T' the corresponding temperature of the vapor; 
 
 h' the difference of level of the two columns; 
 
 t' the temperature of the air. 
 
 Evidently we shall have the equation 
 
 hence 
 
 92 
 
EXPANSION OF GASES 
 
 aT== d + J 
 
 ~ 
 
 for, by reason of the small value of we can always assume 
 
 that t = t. 
 
 I shall again here distinguish as many series of experiments 
 as special pieces of apparatus. 
 
 I. An experiment made to determine the volume of the air 
 reservoir and its coefficient of expansion, gave 
 
 P= 1975.862 gr., 
 p = 29.852, 
 Hi = 745.51 mm., 
 Ti = 99.46, 
 whence 100 6 = 0.002555. 
 
 By measurement, there was found for the weight of mercury 
 filling the capillary tube and the small piece of larger tubing 
 as far as the mark, 
 
 P = 9.740 gr., 
 
 whence P 0.00493. 
 
 P 
 
 The tube being heated by the vapor of boiling water, two 
 readings made with a half-hour interval gave 
 H' ........... 751.01 751.01 
 
 /*' ........... 296.70 296.70 
 
 t' ........... 8.6 8.8 
 
 T ........... 99.66 99.66 
 
 whence H'+h'= 1047.71 1047.71 
 
 The reservoir being in melting ice, we have 
 
 H ........... .749.98 749.88 749.78 
 
 h ............ 20.53 20.59 20.63 
 
 t ............ 8.5 8.5 8.5 
 
 H+h ......... 770.51 770.47 770.41 
 
 We shall take as an average 
 
 H+h = 770.47. 
 
 Comparing this mean with the two determinations at the 
 boiling point of water, we have [the ratios] 
 
 1.36688, 1.36688. 
 
 A second series of experiments made with this apparatus 
 gave: 
 
 The tubes being in melting ice, 
 
 93 
 
ME MO IB 8 OK 
 
 H 746.16 
 
 h 24.53 
 
 t 8.3 
 
 H+ h' 770.69 
 
 746.26 
 24.41 
 
 8.3 
 770.67 
 
 746.39 
 24.21 
 
 8.3 
 770.60 
 
 746.61 
 24.11 
 
 8.3 
 770.72 
 
 746.66 
 
 24.09 
 
 8.3 
 
 770.75 
 
 Mean of H + h = 770.69. 
 
 Iu boiling water we have: 
 
 741.01 
 305.62 
 9.00 
 99.29 
 1046.63 
 
 741.14 
 
 743.20 
 
 743.26 
 
 305.36 
 
 303.72 
 
 303.64 
 
 9.00 
 
 9.00 
 
 9.00 
 
 99.29 
 
 99.37 
 
 99.37 
 
 1046.50 
 
 1046.92 
 
 1046.90 
 
 H' 740.79 
 
 h' 305.58 
 
 *' 9.00 
 
 T 99.28 
 
 H' + h f 1146.37 
 
 On comparing each of the values of H' + li with the mean 
 770.69 of the determinations in melting ice, we have [the 
 ratios]: 
 
 1.36612 
 
 1.36643 
 
 1.36626 
 
 1.36651 
 
 1.36649 
 
 Mean = 
 
 = 1. 
 
 II. With a second apparatus made with a reservoir cut from 
 the same piece of tubing as the former, we have 
 
 assuming 
 
 P= 1817.50 gr.; 
 
 100 (J= 0.002555, 
 
 p* = 8.50 gr., 
 
 P' 
 
 "F = 
 
 0.00468. 
 
 In melting ice we have: 
 
 H. 
 
 t 
 
 H + h.... 
 
 752.60 
 
 752.60 
 
 752.65 
 
 752.57 
 
 752.40 
 
 752.25 
 
 19.58 
 
 19.58 
 
 19.76 
 
 19.66 
 
 19.74 
 
 20.24 
 
 11.0 
 
 11.0 
 
 11.0 
 
 ll.t) 
 
 11.0 
 
 11.0 
 
 772.18 
 
 772.18 
 
 772.41 
 
 772.23 
 
 772.14 
 
 772.49 
 
 Mean of H + h = 772.29. 
 
 In boiling water we have: 
 
 H' 
 
 h' 
 
 If 
 
 751.15 
 
 299.16 
 
 13.7 
 
 1050.31 
 
 99.67 
 
 751.13 
 299.66 
 
 1050.79 
 
 751.13 
 299.66 
 
 1050.79 
 
 751.08 
 299.76 
 
 1050.84 
 
 751.05 
 299.86 
 
 1050.91 
 
EXPANSION OF GASES 
 
 The five values of H' 4- h', compared with the mean of 
 H+h, give [the ratios] : 
 
 1.36672 
 1.36714 
 1.36714 
 1.36730 
 1.36747 
 
 Mean = 6 ' 8 f 77 = 1.36715. 
 5 
 
 Thus the three series of experiments made by this method 
 gave the following mean values: 
 
 1.36688 
 1.36636 
 1.36715 
 
 A 
 
 General mean = *' - = 1.36679. 
 o 
 
 This average differs little from that found in the two former 
 series. 
 
 I do not think this method leads to the same accuracy as the 
 others which I have used. The tubes in which the columns of 
 mercury are measured, are not of large enough diameter to 
 make the capillary effect negligible; the capillary depression 
 amounts in these tubes to about 1 mm. This capillary depres- 
 sion, theoretically, does not enter into the calculation of the 
 constant, and, if it remains always the same, it exerts no influ- 
 ence. Yet it is easy to show that this effect must vary between 
 rather wide limits, by measuring from time to time the heights 
 of the tops of the menisci ; we may thus realize that these 
 sometimes vary in the same experiment from a certain amount 
 to double that amount. As a matter of fact, here is a series of 
 measurements of the corresponding heights of the two menisci: 
 
 Tube EF Tube 00' 
 
 1.08 mm. 1.14 mm. 
 
 0.72 1.64 
 
 1.00 1.64 
 
 1.10 1.32 
 
 1.38 1.36 
 
 0.96 1.20 
 
 0.80 1.18 
 
 It is not possible that such marked variations in the heights 
 of the menisci do not involve very considerable changes in the 
 capillary depressions. 
 
 95 
 
MEMOIRS ON 
 
 Rudberg with his apparatus has found lower figures than 
 mine. It is difficult with any certainty to determine the causes 
 of these differences. I have already stated above that I had 
 never obtained good results when I fixed the mark on the 
 capillary part ED of the tube; but I believe that still another 
 reason could be given which has led Rudberg to results that 
 are too low. This physicist has always in his calculations neg- 
 lected the little volume of air, not heated, which is contained 
 in the portion Ba of his capillary tube. This volume is very 
 small, nevertheless it is hardly probable that it can be entirely 
 neglected. Unfortunately, Rudberg has not given in his mem- 
 oir the dimensions of the different parts of his apparatus; 
 hence it is impossible to calculate now the correction this fact 
 would involve in his results. 
 
 FOURTH SERIES OF EXPERIMENTS. 
 This series of experiments was made with an apparatus 
 
 
EXPANSION OF GASES 
 
 which served the same end as that of the preceding series, 
 without possessing the same disadvantages. It consists of a 
 large bulb A (Figs. 13 and 14) of 800 to 1000 cubic centimet- 
 ers' capacity, to which is sealed a capillary tube about 20 centi 
 meters in length. This bulb serves as the air-reservoir and 
 must be brought successively to and to 100; it is put in 
 communication with a syphon tube full of mercury, which 
 serves to measure the tension of the air. 
 
 A tube JI of 16 to 17 mm. internal diameter, perfectly cyl- 
 indrical, is fastened by means of gum- mastic in an iron cast- 
 ing IH provided with a tap K. This carries a side tubulure H 
 in which is cemented a second tube HGFE of the same diame- 
 ter as the first throughout the length FG. This tube ends at 
 the top in a bent capillary tube FED, cut from the same capil- 
 lary tubing as the tube BC sealed to the bulb. The tube BC 
 fits close in a small copper three-way tube mno in which it is 
 firmly fastened with mastic. In the second arm o is cemented 
 a short piece of capillary tubing op which has been drawn out 
 at its end p. 
 
 The system of the two tubes IJ and EH is fastened to a 
 plank which is itself firmly secured, and in a perfectly vertical 
 position, to a cast-iron upright LL'. 
 
 The bulb A is fastened once for all in a vessel of tin plate 
 MN, in which water can be boiled, or the bulb surrounded 
 with ice. This vessel rests upon an iron, tripod PQQ'P'. A 
 furnace upon a support S can be put below the vessel MN 
 and withdrawn at will. 
 
 This is now the way an experiment is made. The open end 
 of the tube op is connected with the drying apparatus (Fig. 4) 
 [page 75]; and in order to close the arm n of the copper 
 tube, a bit of tubing completely closed is attached to it with a 
 piece of rubber tubing. The water in the vessel MN is 
 brought to boiling, and a vacuum is produced a great many 
 times within the bulb, each time allowing the air to enter again 
 very slowly. 
 
 The tube HGFED had been dried at a high temperature in 
 the same way before being cemented in the tubulure H, and 
 very dry mercury is immediately poured into the tube JI, so 
 as to fill completely the tube ffGFup to the open end D. In 
 
 97 
 
MEMOIRS ON 
 
 this way moisture is kept out of this tube. With the same idea 
 care is taken to keep the end of the tube D covered with a cap 
 of rubber. 
 
 The bulb A being filled with very dry air, the bit of stopped- 
 up tubing, which during the drying was over the tubulure n t is 
 removed, and the capillary tube DE is connected with this tu- 
 bulure by means of rubber; this tube fits closely in the copper 
 tubulure and comes butt-to-butt against the tube BC, so that 
 within, the little copper three-way tube mno the only space 
 there is is the bore of the capillary tubes which meet there. At 
 other times the tube DE is fastened in the tubulure by means 
 of mastic. 
 
 The tap K is opened; the mercury which flows out is re- 
 placed in the tube EFG by air which has passed through the 
 drying apparatus. The mercury is run out until the level 
 stands in the tube FG at a mark a scratched on the glass. The 
 mercury stands at the same level in the two tubes, since on 
 both sides it is freely open to the air. 
 
 The drying apparatus is now disconnected and the tip p of 
 the tube op is closed by means of a lamp. At the same time 
 the height H oi the barometer is recorded. 
 
 The furnace which keeps the water boiling in the sheet-iron 
 vessel is removed. In order that the bulb A may become cool 
 more rapidly, the hot water is drawn off by opening the tap R; 
 the cover abcdefgh is taken off and cold water is poured several 
 times into the vessel to cool the walls. Finally the bulb A is 
 completely covered with crushed ice, which is kept in place by 
 a cloth fastened to the edge cd of the vessel. 
 
 The air contracts on cooling, the mercury rises in the tube 
 GF; but it is maintained at the same level a by running out 
 some of the mercury through the tap K. 
 
 When it is certain that the air in the bulb A has come to 
 the temperature of melting ice, the barometric height H' is re- 
 corded, and the difference of level aP = h' is measured by 
 means of the cathetometer. We thus have already all the 
 data necessary for determining the rate of expansion of 
 air; but we can get a second determination in the following 
 way: 
 
 The closed tip p is again connected with the drying appara- 
 
 98 
 
EXPANSION OF OASES 
 
 tus; "this apparatus is exhausted several times in succession, to 
 make sure that it is full of dry air; then the tip p is broken off. 
 The mercury now falls in the tube FG, but it is brought back 
 to a by pouring mercury into the tube JI. 
 
 After some time the tip^? is again closed by means of a lamp 
 and the height H" of the barometer is recorded. The ice is 
 then removed; the cover abed of the tin vessel is put back, and 
 the water poured into the vessel is brought to boiling once 
 more. By pouring mercury into the tube IJtlcie level is main- 
 tained at a in the tube FG. After the bulb has remained about 
 an hour in [the vapor of] the boiling water, [the height of] the 
 barometer H'" is noted, and the difference of level ay = h'" of 
 the mercury in the two columns is measured. 
 
 In the calculation of the experiment it is necessary to take 
 account of the small volume of air that remains constantly at 
 the temperature of the surrounding air. For this we must 
 know the ratio of this volume to that of the bulb A. The 
 latter volume V had been determined by measurement with 
 distilled water, and the volume v of the air contained in the 
 capillary tubes BC, DEF, op, as well as in the part Fa of the 
 larger tube, had been found by measurement with mercury. 
 We thus had: 
 
 Weight of mercury filling F= 9889.9 gr., 
 ditto ditto v= 26.85; 
 
 hence . = 0.002715. 
 
 I was not able directly to determine the coefficient of expan- 
 sion of the bulb A; it would have been necessary, for this, to 
 have boiled a mass of 9 to 10 kilograms of mercury in a bulb 
 of glass ending in a capillary tube, which seemed to me a prac- 
 tically impossible operation. I have assumed the figure 0.00233 
 for this coefficient, which is the mean of those found for the 
 two bulbs used in my Second Series of determinations. These 
 bulbs were the product of the same factory and were of the 
 same kind of glass. 
 
 The temperatures t, t', t", t"' ', of the small volume of air v 
 were indicated by the small thermometer T' ; that of the col- 
 umns of mercury by the thermometer T whose cylindrical 
 reservoir had the same diameter as the tubes IJ and FG. 
 
 99 
 
MEMOIKS OK 
 
 The equation which serves for the first half of the experi- 
 ment is the following: 
 
 (1 + 6 T) H 
 
 H'-h'- 
 
 + at 
 
 [H II' + /*'] 
 
 that which applies to the second half is 
 
 (l + ST") H'" +h' 
 
 1+ a T" =- 
 
 TJ,, 
 
 -a TT- 
 
 + h'" H"] 
 
 We have assumed in these equations 
 
 t = t' and t" =1"'. 
 
 We now have the figures obtained by this method: 
 
 First Half. 
 
 
 H 
 
 T 
 
 t 
 
 H' 
 
 V 
 
 f 
 
 14 lOOa 
 
 I 
 
 747.83 
 
 99.55 
 
 14.0 
 
 747.43 
 
 197.49 
 
 14.0 
 
 1.36592 
 
 2 
 
 742.27 
 
 99.34 
 
 13.9 
 
 744.25 
 
 198.56 
 
 13.5 
 
 1.36710 
 
 3 
 
 747.97 
 
 99.55 
 
 13.0 
 
 748.52 
 
 198.76 
 
 12.5 
 
 1.36662 
 
 : ^ ^ 
 
 Mean l.J 
 
 Second Half. 
 
 
 H" 
 
 t" 
 
 H'" 
 
 T'" 
 
 h' 
 
 t'" 
 
 1 + 100 a 
 
 1 
 
 747.30 
 
 14.2 
 
 746.45 
 
 99.50 
 
 270.28 
 
 15.1 
 
 1.36682 
 
 2 
 
 744.59 
 
 13.1 
 
 745.27 
 
 99.45 
 
 267.59 
 
 15.6 
 
 1.36674 
 
 3 
 
 748.72 
 
 12.9 
 
 749.19 
 
 99.59 
 
 269.59 
 
 13.9 
 
 1.36580 
 
 Mean.. ..1.36645 
 
 Thus the mean of the six determinations is 1.3665. 
 
 In the Fourth Method the expansion of the air is measured 
 under very different pressures : in fact, in the first half of each 
 experiment the air was under a pressure of only about 0.550 m. 
 when at 0, and under the atmospheric pressure 0.760 m., when 
 heated to 100. In the second half, the air at is under the 
 atmospheric pressure 0.760 m., and the air heated to 100 is 
 under a pressure of about 1.040 m. As the experiments show no 
 difference in the numbers obtained in the two halves, it must 
 be concluded that, within these pressure limits, dry air shows 
 a practically constant coefficient of expansion. 
 
 It is very easy to arrange the apparatus so that it will serve 
 for the study of the expansion of air under greater pressures ; 
 in fact, it will suffice for this to give the tube EFGH & con- 
 siderable capacity from a certain point 6 to H, Fig. 15, sealing 
 the tip p at the time when the bulb as well as the tube EH as 
 far as H are full of dry air, then pouring mercury into the tube 
 
 100 
 
EXPANSI'O'N' OF GASES 
 
 //until the mercury-level coincides with a in the tube FaG, the 
 bulb being surrounded with melting ice ; the mercury then 
 rises in the tube 1J a certain distance h, so that the 
 volume of gas is then at under a pressure H-\-h. 
 The bulb being raised to 100, in order to keep the 
 level of the mercury at a in the tube FG, it is neces- 
 sary to pour a new lot of mercury into the tube //, 
 which gives a difference of level h' and, consequently, E 
 for the pressure upon the gas at 100, H-^li'. The F 
 heights li and h 1 will be more considerable as the a 
 volume of the tube 6H is greater in proportion to 
 the volume of the bulb. Some experiments made by 
 the method thus modified will be discussed later. 1 
 
 1 1 have also made some experiments to determine the 
 coefficient of expansion of air by the method of M. Gay- 
 Lussac. This method consists, as is well known, in observ- 
 ing the expansion suffered by dry air enclosed in an actual 
 thermometer, this air being separated from the outside air 
 by a tiny index of mercury. 
 
 The capillary tube was measured, then graduated with 
 the greatest care ; it was of 2.7 mm. bore and was marked 
 with 600 divisions in a length of 558 mm. The experiment 
 was begun by filling this thermometer with mercury which 
 was again and again brought to boiling in the bulb and in FIG. 15 
 the tube, then was entirely surrounded with ice; the point where the 
 mercury came to rest on the scale was noted. A portion of the mercury 
 in the stem was made to flow out and was weighed,' then the ther- 
 mometer was once more put in the ice and the point noted where the 
 column came to rest. This operation repeated three times in different 
 parts of the scale, gave the following results : 
 
 Mercury at between 375.8 and 602.0 = 226.2 div.; 6.629 gr. 
 103.0 375.8 = 272.8 7.9945 
 
 50.9 499.0 --=448.1 13.128 
 
 From this we deduce for the weight of mercury at occupying owe 
 division : 
 
 in the first interval ........ ............ 0.029306 gr. 
 
 in the second ......................... 0.029305 
 
 in the third ............... ........... 0.029297 
 
 Mean = o_jL8_72JLS. = 0.029303. 
 
 The close agreement to be noticed in these figures proves satisfactorily 
 the accuracy of the graduation. 
 
 The mercury which at filled the bulb and the stem as far as divi- 
 sion 50.9, weighed 27.916 gr. 
 
 101 
 
l$ ON 
 
 The four series of experiments which I have described in 
 detail have therefore given the following averages : 
 
 After the mercury has been completely removed from the apparatus, 
 it is connected by means of rubber tubing with a U-shaped tube con- 
 taining pumice stone moistened with sulphuric acid and is exhausted a 
 great many times while being warmed by means of hot coals. This 
 thermometer tube was fitted at the end with a bit of larger tubing in 
 which had been left a tiny drop of mercury to form the index. The 
 apparatus being filled with dry air, the bulb is raised to such a tempera- 
 ture that the globule of mercury, when drawn into the capillary tube, 
 comes to rest at a convenient point when the thermometer is placed in 
 melting ice. 
 
 The greatest pains were taken to place the stem of the thermometer 
 in a perfectly horizontal position where the instrument was in ice or in 
 [the vapor of] boiling water, and it was given light taps to assist the 
 movement of the index. 
 
 I shall not describe in detail the numerous experiments made by this 
 method ; suffice it to say I was unable to get constant figures. The way 
 in which the thermometer tube was tapped, the points on the tube 
 where it was struck, produce a very marked effect upon the position of 
 the index. The movement of the index even seemed to depend upon 
 the more or less rapid changes of the temperature, which seems to show 
 that the mercury index does not close the tube perfectly, and that 
 would not be surprising after what we have seen above [page 80]. 
 What confirms me in this opinion is that, in many experiments, the 
 index did not return to the same point, the thermometer being sur- 
 rounded with ice, when, in the interval, the apparatus had been heated 
 to the boiling point of water. 
 
 Thus, in one experiment, the index came to rest when the 
 thermometer was in ice, at 152.7 div. 
 
 In [the vapor of] boiling water at 534.5 div. ; the appara- 
 tus being again surrounded with ice, the index came to rest at. .154.5 div. 
 and meantime the barometer had not changed to any noticeable extent. 
 
 In another experiment the index came to rest in melting ice at 66.5 
 div. before the instrument had been put in [the vapor of] boiling water, 
 and at 66.0 div. after it had been heated. The barometer had changed 
 in a very marked way during the interval, but this change should have 
 produced a movement in the opposite direction. 
 
 However that may be, here are some of the figures I obtained by this 
 method : 1.3641 
 
 1.3626 
 1.3635 
 1.3647 
 1.3552 
 
 It is remarkable that all these figures are smaller than those yielded 
 by the other methods. This circumstance is probably the result of mere 
 chance. 
 
 102 
 
EXPANSION OF GASES 
 
 First series ................................ 1.36623 ; 
 
 Second series .............................. 1.36633 ; 
 
 Third series ............................... 1.36679 ; 
 
 Fourth series .............................. 1.36650 ; 
 
 That is to say, about ..................... 1.3665. 
 
 I therefore propose to adopt for the coefficient of expansion 
 of dry air for each degree centigrade between the two fixed 
 points of the thermometer, 0. 003665. 1 
 
 We shall now proceed to take up in succession all the quan- 
 tities which enter into the calculation of the experiments, in 
 order to obtain an approximate value, at least, for the error 
 each of them may introduce. 
 
 The equation 
 
 P'(l+*T)H 
 
 ~(P' P) (H'h)\ 
 
 which applies to the first two series, comprises the weights P 
 and P' of mercury which can be determined with what may be 
 called absolute precision. Thus the factor p f_ p cannot intro- 
 duce any noticeable error arising from its experimental deter- 
 mination. 
 
 The factor 1 -\-6T depends upon the expansion of the glass. 
 We have seen that this expansion was determined for each ap- 
 paratus by direct experiment and it must be admitted to be 
 rigorously exact; besides, since it is very small, a noteworthy 
 error in this coefficient would exert no appreciable effect upon 
 the value of the coefficient of expansion of air. 
 
 The coefficient of expansion of glass was determined as being 
 a function of the coefficient of expansion of mercury; I have 
 assumed for the latter coefficient the value ^. 5 = 0.01802, 
 found by Dulong and Petit. Unfortunately, some uncertainty 
 exists regarding the numerical value of this coefficient; in fact, 
 Dulong and Petit gave in their memoir only the following 
 values: 
 
 Expansion of mercury for each degree centigrade between 
 
 and 100, 
 ditto ................ ditto ...... and 200, 
 
 ditto ................ ditto ....... and 300, 
 
 1 M. Babinet has called my attention to the fact that, adopting for the 
 coefficient of expansion of air the figure 0.366666. . . , this coefficient 
 may be represented by the very simple fraction fo, which is very easy to 
 use in calculations. 
 
 103 
 
MEMOIRS ON 
 
 The temperatures are given here, as these distinguished phys- 
 icists explicitly state, with reference to the air thermometer, 
 assuming for the coefficient of expansion 0.375; but if this co- 
 efficient is inaccurate and if the figure 0.3665 must be used, 
 then the intervals of temperature change appreciably and the 
 temperature 100 of Dulong becomes 102.7 , so that the coeffi- 
 cient 5^ should be about -fa greater. 1 
 
 It is possible, however, that the coefficient of absolute expan- 
 sion of mercury between and 100 given by Dulong and 
 Petit may be that which they found directly in their experi- 
 ments from [the temperature of] melting ice up to [that of] 
 boiling water, without deducing it from their interpolation-for- 
 mula. In this event it would not be affected by the same 
 source of error as the values between and 200 and between 
 and 300. However that may be, new experiments alone 
 can decide the point. 
 
 What interests us at this moment is to see what difference 
 this could bring about in our coefficient of expansion of air. 
 Assuming the coefficient of absolute expansion of mercury be- 
 tween and 100 too great by -fa, the coefficient of expansion 
 of glass would be too great by about -j^. Thus, instead of the 
 figure 1.0026, we should have in the numerator the figure 
 1.0024, smaller than the former by T o,^o, which would reduce 
 the figure 1.3665 by y^oo* that is to say, would give 1.3662; 
 consequently this change would affect only the fourth decimal: 
 after all, it is a correction easily made in all my figures. 
 
 TT 
 
 The factor H ,_ h which depends upon the barometric mea- 
 surements, is the one which is liable to the largest errors of ob- 
 servation. Physicists who have had occasion to make a large 
 number of barometric observations, know how difficult these 
 observations are when the attempt is made to reach the high- 
 est limit of accuracy. I do not believe I exaggerate when I 
 take it for granted that a barometric reading cannot be made 
 closer than ^ of a millimeter, however improved the measur- 
 ing apparatus may otherwise be. The difficulty lies in the fact 
 that the atmospheric pressure is constantly changing, bat this 
 
 i This point has already been made by M. Poggendorif, Poggendorff's 
 Annalen, Yol. XLI, page 467. 
 
 104 
 
EXPANSION OF GASES 
 
 variation is at once shown by the barometer, yet as a rule, 
 only the changes in the form of the meniscus, and the varia- 
 tions in height do not take place in any regular way, but 
 rather by jerks. It is well, in order to avoid this trou- 
 ble, to tap the barometer to make the mercury column 
 move back and forth, before making a reading, yet it is 
 clear that the source of error is not completely done away with 
 by this means. 
 
 Each of the measurements H, H', h, is liable to the same er- 
 ror e. In order to determine the maximum deviation of indi- 
 vidual experiments, we shall suppose the errors made in H, H', h, 
 to have such signs as will produce the greatest difference in 
 the final result. Thus, we will assume that instead of the 
 
 rr 
 
 accurate factor H ,_ fl , observation has given us the factor 
 
 H+e 
 
 (H'-e) - 
 
 The error is then represented by 
 
 or 
 
 e (2 ff4 H' h) 
 
 (H'h) (H' h-2e) 
 or simply 
 
 2H+H' h 
 (H' h)* ' 
 
 by neglecting 2e in the denominator in comparison with H' h. 
 As a result, the value of 1 + aT becomes 
 
 , a 
 
 _ 
 (P' P) JET h I- H' h 
 
 Assuming H = H' = 760 mm., h = 190 mm.; we shall have 
 for the last factor 
 
 760.00 mm. + e. 209 , 
 or 570 ' 
 
 760.00 mm. + e x 3.67. 
 
 If e = 0.1 mm., then the total error resulting for 760.00 mm. 
 will be 0.367 mm., that is to say T<To*Wo- 
 
 This gives for the total possible range of error in the experi- 
 ments, for this source of error alone, -njofinny- 
 
 It may thus be seen that if we assume it impossible to attain 
 H 105 
 
MEMOIRS ON 
 
 an accuracy greater than ^ of a millimeter in barometric ob- 
 servations, the determinations of the rate of expansion of air 
 will be liable, from this source of error alone, to show a maxi- 
 mum variation, of about T ^oo Ik will be noticed that this is 
 close to the maximum variation to be observed in my results. 
 
 In order that the coefficient of expansion of air may be exact 
 up to the third decimal, the experiment which determines it 
 must not lead to an error of more than T ^oo- The direct ex- 
 periment does not tell us, as a matter of fact, that 1000 parts 
 of air expand between and 100 by 366 parts, which would 
 be an accuracy of only ^^; but rather that 1000 parts of air 
 become 1366 in passing from to 100, which gives an accu- 
 racy of jsVe. 
 
 The formulas which apply to the two later series of experi- 
 ments are evidently open to the same sources of error. The 
 possible error in the measurement of the heights of the col- 
 umns of mercury is probably even greater in the apparatus of 
 the Third Series, since the tubes are narrower and on this ac- 
 count show a greater variability in the capillary depression. 
 
 Yet there is in addition another source of uncertainty in 
 these two methods which did not enter into the two earlier 
 ones: it lies in the determination of the temperature of the vol- 
 ume of air which was not heated. The error resulting from 
 this might be quite large if this volume formed an appreciable 
 fraction of that which is brought to the fixed points: it is en- 
 tirely negligible in my experiments, since I took pains to carry 
 them out so that the volume of the air that was not heated 
 should never be but an extremely small fraction of the total 
 volume. 
 
 The temperature ^of the vapor was calculated from the ob- 
 served barometric heights at the time of the boiling. I have 
 assumed in this calculation that a variation of 1 in the boiling- 
 point of the water corresponded to a difference of pressure of 
 26.7 mm. This figure is that given in the tables of the tensions 
 of water-vapor recently calculated by M. Biot. It seemed to 
 me better to adopt this figure, than to take the numbers found 
 by different physicists by determining with some one ther- 
 mometer the boiling point of water under various barometric 
 pressures. These experiments could not result in great accu- 
 
 106 
 
EXPANSION OF GASES 
 
 racy, for they were frequently carried out on days quite sepa- 
 rated from one another, and because the instrument had 
 probably already suffered some appreciable change in the inter- 
 val through the movement of the fixed points. 
 
 In order that these experiments should yield results that 
 could not be questioned, it must have been possible to take 
 note of the boiling point of water under various pressures, at 
 times close together, for example, in an apparatus where the 
 pressure could be varied at will, as in the apparatus of M. 
 Tabarie. A series of observations might even be made during 
 the ascent of a mountain and while care was being taken to 
 keep the thermometer constantly in [the vapor of] boiling 
 water during the ascent, in order to avoid as far as possible 
 movement of the fixed points. 
 
 However that may be, the figure I have assumed must be 
 very near the true one, and the error which could be produced 
 by it in the coefficient of expansion of air is entirely inappre- 
 ciable. 
 
 My barometric observations were made with a barometer with 
 a Fortin cistern, which had been carefully compared in a series 
 of measurements, with that of .the Paris Observatory, corrected 
 for capillary depression, and all my observations were reduced 
 by calculation to [those of] the Observatory barometer. 
 
 After all, a small constant difference in the absolute values 
 of all the barometric heights would have had no appreciable 
 effect upon the coefficient of expansion of air, since it would 
 have had to do only with the determination of the temperature 
 of the vapor, and its influence upon the other would be quite 
 inappreciable. 
 
 PAET II. 
 
 Upon the Rate of Expansion of certain other Gases. 
 
 The old coefficient adopted for the expansion of air being in- 
 accurate to the extent of ^, it is clear that it cannot be con- 
 sidered as proved that all gases have the same coefficient of 
 
 107 
 
MEMOIRS ON 
 
 expansion; new determinations are necessary to decide whether 
 this law is strictly true or is only approximate. 
 
 I have made experiments upon nitrogen, hydrogen, oxide of 
 carbon [carbon monoxide], carbonic acid, sulphurous acid, 
 cyanogen, protoxide of nitrogen [nitrous oxide], hydrochloric 
 acid and ammonia. Most of these determinations were made 
 by Method II; some however were made by Method IV. 
 
 First, I shall describe in a few words how the experiment 
 was managed when Method II was employed. The bulb being 
 suspended in the steam vessel and connected with the drying- 
 apparatus, it was exhausted many times and the. air allowed to 
 re-enter slowly, in such a way as to dry the bulb thoroughly; 
 then to the second tubulure of the pump was attached the 
 apparatus in which the gas was produced. The bulb being 
 exhausted, as well as the gas-generating apparatus, the tap is 
 gradually opened so as to allow the gas to enter as fast as it is 
 formed : the progress of the operation is indicated by a safety 
 tube placed somewhere in the generating apparatus. When 
 the bulb was full of gas, it was exhausted, then allowed to be- 
 come full of gas once more, and so four or five times in succes- 
 sion. In other respects the experiment was conducted as has 
 been described [page 84]. 
 
 In these determinations Bulb VI [page 88] was used, and 
 two new bulbs, VII and VIII, for which the following data 
 were obtained: 
 
 Bulb VII. Bulb VIII. 
 
 P= 4358. 15 gr. 4250. 70 gr. 
 
 p = 67.17 65.10 
 
 H\ = 753.62 mm. 752.68 mm. 
 
 T\ = 99.76 99.73 
 
 Whence 100 6 = 0.002291 0.002385 
 
 c= 0.10mm. 0.10mm. 
 I have brought together in a single table the results obtained 
 by this method with different gases. 
 
 108 
 
EXPANSION OF GASES 
 
 lO CO Q (NC^t <Nt CO^i ICOGOC^OOOOiMGOt O ^ O lO 
 
 CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO 
 ooo ooooooooooooooooooooo 
 
 O O Oi Oi Oi Oi O O Oi Oi Oi Oi Oi Oi Oi O O Oi Oi Oi Oi O O 
 
 OO OiOiOiOiOOOiOiOiOiOiOiOiOOOiOiOiOiOO 
 
 o p p o p p p "* ppp^p^pp^pp 
 
 JC^ ^ 
 lr** CO iO 
 
 05 CO CO 
 GO ** *& 
 
 tr53^^I^^^5S5S^rfcrS)5 <? ^ ' 1 ^ 
 
 Oi O Oi Oi GO Oi Oi Oi Oi O Oi Oi Oi Oi O Oi Oi 
 
 01 r- co 
 
 rH GO t^ 
 
 o T-H 5 
 
 CO CO CO - _. _. 
 
 t- t- t- t- t- t- 
 
 co 
 
 <D 
 
 s 
 
 * p 
 
 o 
 
 CO t- 
 
 109 
 
MEMOIKS ON 
 
 I shall add a few words upon the way in which each gas was 
 prepared. 
 
 1. Nitrogen. This gas was obtained by removing the oxygen 
 of the air by passing it through a glass tube filled with copper 
 turnings 1 heated to redness. This tube was connected with 
 the tubulure of the pump. The bulb having been exhausted, 
 the tap is opened little by little; the air in passing over the hot 
 copper loses its oxygen and, later, gives up its moisture in the 
 drying tubes. 
 
 2. Oxygen. I made many experiments upon oxygen gas, but 
 they yielded figures so various that it was impossible to reach 
 any decision from them. Mercury cannot be left in contact 
 with oxygen gas, even for a very short time, without absorbing 
 a small amount of the gas: its surface soon gives evidence of 
 mercury oxide and leaves a trail on the glass tube. 
 
 The same thing is noticed with mercury which is left in con- 
 tact with the air, but the change in this case is much slower, 
 requiring a period of several weeks to become appreciable. 
 
 The oxygen was prepared by heating potassium chlorate. 2 
 
 3. Hydrogen. This gas was prepared by treating zinc with 
 dilute sulphuric acid ; before entering the pump and the dry- 
 ing apparatus, it was passed through two tubes, a meter long, 
 filled with pumice stone moistened with a solution of caustic 
 potash, and a third tube filled with pumice stone moistened 
 with a solution of silver sulphate. The gas was entirely with- 
 out odor. The introduction of the two tubes of pumice soaked 
 in a solution of potash is chiefly to hold back the small quan- 
 tity of odorous oily vapor which hydrogen gas always takes 
 with it and which is sufficient to change appreciably the expan- 
 sibility of the gas. In fact, in one experiment where the 
 hydrogen gas passed merely through a wash bottle containing 
 water, I found for its coefficient of expansion the figure 0.3686; 
 
 1 The copper turnings were first oxidized by heating in the pres- 
 ence of air, then reduced by a current of hydrogen gas. 
 
 2 Note by Translator : It seems likely that Regnault's oxygen was 
 not pure possibly contained chlorine, or oxides of chlorine; v. Jolly 
 states that oxygen carefully prepared from potassium chlorate, or elec- 
 trolytically, is entirely without action on mercury at the temperature of 
 the experiment. 
 
 110 
 
EXPANSION OF GASES 
 
 a second determination in which the wash bottle contained pot- 
 ash-solution, gave the figure 0.3679. 
 
 4. Oxide of Carbon. Prepared by decomposing oxalic acid 
 in the presence of concentrated sulphuric acid: the gas was 
 passed through a flask containing a solution of caustic potash 
 to absorb the carbonic acid, then through a long tube filled 
 with pumice stone moistened with potash solution; from this it 
 passed into the drying apparatus. 
 
 5. Carbonic Acid. Obtained by the decomposition of white 
 marble with dilute hydrochloric acid. The gas passed through 
 a wash bottle containing water and thence into the drying 
 apparatus. 
 
 6. Cyanogen. This gas was prepared through the decompo- 
 sition by heat of cyanide of mercury contained in a small glass 
 retort; it passed through a flask provided with a safety tube 
 and filled with concentrated sulphuric acid, which serves to 
 regulate the flow of the gas. 
 
 7. Protoxide of Nitrogen. The protoxide of nitrogen was 
 prepared by decomposing with the aid of heat ammonium 
 nitrate contained in a retort. The gas, before entering the 
 drying tubes, passed through a wash bottle containing a solu- 
 tion of protosulphate of iron [ferrous sulphate]. 
 
 8. Sulphurous Acid. This gas was prepared by heating mer- 
 cury with concentrated sulphuric acid. The gas passed through 
 a wash bottle containing concentrated sulphuric acid, then the 
 usual drying apparatus. 
 
 9. Hydrochloric Acid Gas. Obtained by treating sea salt 
 with concentrated sulphuric acid; it was passed through a 
 flask containing concentrated sulphuric acid, then through 
 two tubes full of pumice stone soaked with sulphuric acid. 
 
 The experiments upon hydrochloric acid gas present nothing 
 out of the way. The mercury retained its brilliant surface. I 
 cannot have entire confidence, however, in the results obtained. 
 In fact, mercury is apparently not attacked by hydrochlorie 
 acid gas by itself, but it is very quickly [attacked] as soon as 
 the gas is mixed with oxygen. It is conceivable that a few 
 thousandths of air, mixed with the hydrochloric acid gas 
 in the bulb, would serve to bring about a very perceptible 
 
 111 
 
MEM OIKS ON 
 
 absorption of gas and in consequence to interfere with the 
 expansion. 
 
 10. Ammonia Gas. Prepared by gently heating a concen- 
 trated aqueous -solution of the gas. It passed through a 
 tube a meter long, filled with caustic potash broken in small 
 pieces. 
 
 Ammonia gas yielded most various figures. The mercury 
 seemed to be greatly changed at the surface: it left a trail: 
 there had evidently been an absorption of gas; but it has been 
 impossible for me to determine the chemical reaction which 
 took place. 
 
 I found in succession the figures 0.370, 0.371, 0.373, accord- 
 ing as the gas had remained a longer or shorter time in contact 
 with the mercury. 
 
 It will be seen in the table above that nitrogen, hydrogen, 
 oxide of carbon have practically the same coefficient of 
 expansion as air, under the conditions when the determina- 
 tions were made, that is to say, the gases being under atmos- 
 pheric pressure when they are at the boiling point of water, 
 and under a pressure of about 550 millimeters when they are at 
 the melting point of ice. 
 
 Carbonic acid, protoxide of nitrogen and cyanogen, on the 
 contrary, show under the same circumstances a greater coeffi- 
 cient of expansion. 
 
 Sulphurous acid gas gave figures a little higher than those 
 obtained for the above gases; but the difference is so small 
 that one does not know whether it may not be due to the inev- 
 itable errors of experiment. 
 
 I do not discuss hydrochloric acid gas, since I look upon the 
 numbers obtained for this gas as doubtful. 
 
 My experiments therefore seem to show that gases do not 
 have, under the same conditions, exactly the same coefficient of 
 expansion. This coefficient varies for the gases I have exam- 
 ined, and with the conditions under which the determinations 
 were made, from 0.3665 to 0.3685. 
 
 This variation cannot be attributed to the fact that, at the 
 temperature of melting ice and under a pressure of 0.555 m., 
 certain of these gases are close to their point of condensation; 
 for sulphurous acid is, of all these gases, the easiest to liquefy 
 
EXPANSION OF GASES 
 
 and yet its coefficient of expansion is smaller than that of car- 
 bonic acid which at is still removed by more than 90 from 
 its condensation point. 
 
 This modification, which must be made in one of the most 
 beautiful laws of physics, seemed to me too important for me 
 not to endeavor to support it by other determinations. 
 
 I began by making several experiments with Method 
 using exactly the same apparatus as had been used for air. 
 
 For carbonic acid gas I obtained the following results: 
 First Half. 
 
 IV, 
 
 H 
 
 T 
 
 t 
 
 H' 
 
 h' 
 
 V 
 
 l+100a 
 
 756.52 
 
 99.87 
 
 13.4 
 
 755.47 
 
 200.58 
 
 13.0 
 
 1.36831 
 
 757.54 
 
 99.91 
 
 12.9 
 
 758.02 
 
 202.55 
 
 11.7 
 
 1.36857 
 
 Second Half. 
 
 Mean = 1.36844 
 
 H" 
 
 t" 
 
 H'" 
 
 T" 
 
 h'" 
 
 t?" 
 
 758.47 
 
 11.8 
 
 758.80 
 
 99.95 
 
 275.67 
 
 14.8 
 
 758.47 
 
 11.8 
 
 759.10 
 
 99.97 
 
 275.51 
 
 14.1 
 
 1 lOOa 
 1.36846 
 1.36866 
 Mean = 1.36856 
 
 These determinations give at least nearly the same figure as 
 that found by Method II. 
 
 An experiment made with protoxide of nitrogen gave : 
 FIRST HALF. SECOND HALF. 
 
 H =747.03 mm. 
 
 T = 99.52 
 t = 4.2 
 
 T= 748.08 mm. 
 h'= 198.39 mm 
 t' = 3.6 
 1+100 a = 1.36701 
 
 H"= 747.72 mm. 
 
 r= 3.6 
 
 H"= 748.49 mm. 
 T"= 99.57 
 h''== 269. 73 mm. 
 "'= 3.9 
 1+100 a = 1.36797 
 
 Mean = 1.36749 
 
 The mean given by the determinations described above and 
 made by Method II, is 1.36763. 
 
 We have seen that Method II gave for the coefficient of expan- 
 sion of sulphurous acid a figure practically identical with that 
 found for air. I wished to find out whether this coefficient 
 would not become larger when working under greater pres- 
 sures. 
 
 An experiment made with sulphurous acid by Method IV, 
 gave : 
 
 113 
 
MEMOIRS ON 
 
 FIBST HALF. SECOND HALF. 
 
 H = 742.08 mm. H" = 742.49 mm. 
 T= 99.33 t" = 5.3 
 
 t = 5.6 H"' = 742.85 mm. 
 
 H= 742.31 mm. T" = 99.36 
 
 h'= 196.64 mm. h'" = 267.64 mm. 
 
 t'= 4.5 '" = 6.6 
 1+100 a = 1.36689 1-flOO a = 1.36777 
 
 The figure obtained in the first half of the determination is 
 identical with that found in the experiments made by Method 
 II, whereas that given by the second half, that is, under 
 greater pressures, is notably greater. 
 
 A second trial was made by subjecting the sulphurous acid to 
 a little more than atmospheric pressure when the gas was at 
 0. The bulb was surrounded with ice and the side tube put 
 in communication with the apparatus generating sulphurous 
 acid gas, when the mercury was run out by opening the tap, 
 so as to let the tube FH become entirely filled with sulphurous 
 acid gas. The tubej9 was then sealed with a lamp. Mercury 
 was poured into the tube G, so as to bring the level to a in the 
 tube FH. A difference of level h is then noted between 
 the two menisci. The ice was removed and the bulb raised to 
 the boiling point of water, as in the ordinary determinations. 
 We thus have : 
 
 H 743.59mm. 
 
 t 5.6- 
 
 h 28.69mm. 
 
 H 743.92mm. 
 
 T 1 99.40 
 
 h' 308.22mm. 
 
 t 6.1 
 
 1+100 a 1.36907 
 
 Finally, a third determination was made subjecting the gas 
 to a much higher pressure still. For this the tube FH was 
 replaced by another, the lower part of which had a much 
 greater volume. This tube is shown in Fig. 15 [page 101]. 
 
 Working exactly as in the second determination, we find : 
 
 114 
 
EXPANSION OF GASES 
 
 H = 764.77 mm. H' = 764.64 mm. 
 
 t = 5.9 T' = 100.17 
 
 h = 136.29 mm. h' = 469.71 mm. 
 
 t'= 7.00 
 
 _H_ =.00336 
 V 
 
 whence 
 
 l+100a = 1,37413. 
 
 Thus for sulphurous acid the results are : 
 
 The gas at under At 100 under 
 a pressure of a pressure of 
 
 545.67mm. 742.08mm. 1J 
 
 742.49 1010.49 1.36777 
 
 772.28 1052.14 1.36907 
 
 901.06 1234.35 1.37413 
 
 The coefficient of expansion of sulphurous acid therefore 
 increases in a very marked way in proportion as the pressure to 
 which the gas is subjected becomes greater. It is probable that 
 the same thing takes place in all compound gases for which the 
 law of volumes does not rigorously hold or which do not exactly 
 follow Mariotte's Law. 
 
 A similar variation is to be noticed in carbonic acid gas, 
 although in a much less decided way. We have seen that 
 Method IV, applied to this gas, gave : 
 
 Pressure at At 100 
 
 554.89 mm. 756.52 mm. 1.36831 
 
 555.47 757.54 1.36857 
 
 758.47 1034.47 1.36846 
 
 759.10 1034.61 1.36866 
 
 The difference is not noteworthy. But an experiment made 
 with the modified apparatus which I have described, gave : 
 
 H = 766.32 mm. H 1 = 766.14 mm. 
 
 t = 6.4 T' = 100.23 
 
 h = 134.77 mm. t 1 = 6.4 
 
 h< = 464.23 mm. 
 v 
 -y- = 0.00336. 
 
 1 + 100 a =1.36943. 
 115 
 
MEMOIRS ON 
 
 Thus, at under a pressure of 901.09 mm. and at 100 
 under a pressure of 1230.37, the coefficient of expansion of car- 
 bonic acid gas is distinctly higher. 
 
 I have constructed an apparatus by means of which one may 
 at once detect unequal expansion in gases and which may serve 
 to measure this difference with accuracy. This apparatus, 
 which is a kind of differential thermometer, consists of two 
 bulbs of equal capacity, complete with capillary tubes and 
 arranged exactly like the bulb of Method IV (Fig. 13), [page 
 96]. Each of these bulbs connects with a tube similar to the 
 tube FH of Figs. 13 and 14, cemented into a three-way tube 
 of iron provided with a tap, Fig. 16. The third branch, in the 
 middle, holds a piece of barometer tubing. The 
 two tubes FGH and F'GH' were cut from the 
 same accurately cylindrical piece of tubing and 
 have exactly the same shape ; they are fixed as 
 alike as possible in the tubulures. One of the 
 bulbs is filled with dry air and the other with the 
 gas whose expansibility it is desired to compare 
 with that of air. Moreover, the bulbs are fast- 
 ened in the same tin vessel. 
 
 The bulbs being surrounded with melting ice, 
 and the mercury having been adjusted to the 
 Cf\ YG' level of a mark scratched on one of the tubes, 
 the two side tubes op are closed with a lamp. 
 The mercury is then of necessity at the same level 
 in the two tubes FGHand F'G'H' and in the up- 
 right tube between them. The ice having been 
 removed and water put in the tin vessel, the 
 latter is brought to boiling while mercury is 
 1|)K- poured into the intermediate tube to keep the 
 FIG. 16. level at the same point in the tube FGH. If 
 the two gases have the same coefficient of expansion, the two 
 menisci in the tubes FGH and F'G'H' will be at the same 
 level ; there will be a difference of level, on the other hand, if 
 the [rates of] expansion are unequal. 
 
 It would be very difficult to find two bulbs of exactly the 
 same capacity when they are sealed to their capillary tubes, 
 
 116 
 
EXPANSION OF GASES 
 
 and also so to arrange the tubes FGH and F'G'H 1 that the vol- 
 ume of air contained in the upper part'of these tubes should be 
 exactly equal when the mercury is at the same level and 
 adjusted to the mark made on one of them. Yet this is not 
 necessary ; it will, in fact, serve if the ratio -^- is the same for 
 the two pieces of apparatus. It will do, indeed, for this to 
 take two bulbs of nearly the same volume and gauge them 
 carefully by means of distilled water, after they have been 
 attached to their capillary tubes. In the same way the tiny 
 volume in the part Fa of the tube FGH us far as the mark a, 
 is measured by means of mercury; on the other tube F'G'H' are 
 made two marks, a' and a", and the volume up to a" and that 
 between the two marks a and a", are calibrated by means of 
 mercury. 
 
 This done, we know the ratio ^ f or the first bulb, and the 
 volume V' of the second bulb; then v 1 must be equal to 
 -2=> V. It is easy to find the point on the tube G' H f which 
 corresponds to this volume v' ; its distance d from the mark a< 
 is then calculated. 
 
 The tube FGH being cemented in its tubulure and the 
 apparatus fastened to its vertical support, the tube F'G'H 1 is 
 fixed in the place where it belongs. For this purpose, the level 
 of the mark a upon the tube FGH is found with the cathetom- 
 eter, and the glass is then turned towards the tube F'G'H 1 . 
 If the latter tube is in the proper position, the crossing of the 
 threads of the glass should be aiming at the point which cor- 
 responds to the volume V 1 ; consequently the mark a! should be 
 at a distance d above or below ; by means of the instrument we 
 find whether this is in fact the case, that is, the glass is raised 
 or lowered by an amount d, and the tube F'G'H' is adjusted so 
 that the mark a' is hidden by the horizontal thread of the glass 
 in its new position ; then the tube is fastened in place with 
 mastic. 
 
 To make sure that the differential apparatus is properly 
 adjusted, an experiment is made, filling both bulbs with dry 
 air. The two side tubes op are closed when the bulbs are in 
 melting ice and the mercury has been brought to the level of a 
 
 117 
 
MEM OIKS ON 
 
 in the tube FGH. The three columns of mercury are then at 
 the same level. Water is then put in the boiler and the level 
 of the mercury is kept at a; the mercury must be at exactly the 
 same height in F'G'ff' if the apparatus is properly put together. 
 
 The results reached by this method are rendered still more 
 certain by performing a second experiment in which the gas 
 whose expansibility we wish to determine, is introduced into 
 the bulb which has hitherto held the air, while, on the other 
 hand, atmospheric air is put in the bulb which in the former 
 experiment contained the gas. 
 
 The equation which gives the expansibility of the gas in the 
 case of this apparatus is clearly 
 
 the symbols having the same meaning as on page 100. 
 
 If we diiferentiate with respect to a and Ji" 1 , bearing in mind 
 
 that the factor^- 5_ (ff" f + h' l( H") is very small and may 
 be supposed contant and equal to &, we have 
 
 we can then write it simply 
 
 - 
 
 That is, the difference in the coefficients of expansion of the 
 two gases is equal to the difference in the levels of the columns 
 of mercury in the two tubes FGH and. F'G'H', divided by the 
 barometric height at the time the two tubes were sealed when 
 the bulbs were in melting ice. 
 
 This result is not however altogether accurate, since we have 
 
 taken no account of the variation of the ratio ^ which is 
 not the same at 100 as at for the gas which does not 
 expand at the same rate as air. But when the difference in the 
 ratio of expansion is very slight, the error introduced by this 
 omission is practically inappreciable. On the other hand, it is 
 easy to take it into account. 
 
 118 
 
EXPANSION OF GASES 
 
 A test determination made by this method with carbonic acid 
 gas and atmospheric air, gave 
 
 A h"' = 1.48 mm., //" = 757.20; 
 hence 
 
 A a = ' 757 ' = 0.002 (about) ; 
 
 that is, the coefficient of expansion of carbonic acid gas is 0.002 
 higher than that of air which gives 0.3685; and this, in fact, 
 is the figure which we found above [page 113]. 
 
 To prove the accuracy of the differential apparatus, I filled 
 both bulbs with dry air; I then found 
 A h'" = 0.08 mm. 
 
 This difference is probably due to the fact that the tubes 
 were not quite perfectly adjusted, but it is entirely inappreci- 
 able. 
 
 119 
 
EXPANSION OF GASES 
 
 BIOGRAPHICAL SKETCH. 
 
 Henri Victor Eegnanlt was born at Aix la Chapelle in the 
 year 1810, July 21. He was educated at the Ecole Poly tech- 
 nique and the Ecole des Mines. He became Gay-Lussac's suc- 
 cessor as Professor of Chemistry in the former institution in 
 1840, and, the next year, Professor of Physics in the College de 
 France. Up to this time his researches were confined to 
 organic chemistry: an important paper on the ethers appeared 
 in 1835. From 1847 to 1854 he was Chief Engineer of Mines, 
 and subsequently became director of the famous porcelain 
 works at Sevres. From 1841, for over twenty years, he published 
 the results of research after research upon the physical con- 
 stants of gases, of liquids and of solids. In this extraordinary 
 series are to be found investigations of the compressibility of 
 gases, liquids and solids; of their densities, and rates of expan- 
 sion; of the tension of vapors; of calorimetrical methods; of 
 the latent heat of substances; of their specific heat, etc., etc. 
 In addition, may be mentioned contributions to the mechanical 
 theory of heat and study of the velocity of sound. All the 
 records of his latest work were, to his great sorrow and to 
 the loss of the scientific world, destroyed during the Franco- 
 Prussian War. His scientific labors ended in 1872, but he 
 lived until Jan. 19, 1878. Regnault's great reputation rests 
 upon his extraordinary skill in devising and using apparatus. 
 It may be said that in whatever direction his researches led 
 him, he invariably succeeded in discovering sources of error in 
 the work of his predecessors and in eliminating it, at least in 
 large measure, from his own results. 
 
 120 
 
RESEARCHES UPON THE EXPANSION 
 
 OF GASES. 
 
 BY HESTRI VICTOR EEGNAULT. 
 Second Memoir. 
 
 121 
 
CONTENTS. 
 
 PAGE 
 
 Object . . . . . . . . . 123 
 
 Experiments under pressures less than the atmospheric: 
 
 Method 124 
 
 Results 126 
 
 Experiments under pressures greater than the atmospheric: 
 
 Method 127 
 
 Apparatus 127 
 
 Results 134 
 
 Application of method to Carbon dioxide . .136 
 
 Expansion of Gases under Constant Pressure: 
 
 Importance of research 136 
 
 Apparatus and manipulation .... 138 
 Results ivith air . . . . . , .143 
 
 Results with hydrogen 143 
 
 Results with other gases ..... 143 
 
 Errors discovered in results of First Memoir . . . 145 
 
 Comparison of results, constant volume and constant 
 
 pressure 148 
 
 Conclusions . 150 
 
 122 
 
RESEARCHES UPON THE EXPANSION 
 
 OF GASES. 
 
 BY M.VICTOR REGKAULT. 
 Second Memoir. 
 
 IK a former treatise (Annales de Ghimie et de Physique, 3d 
 Series, volume IV, page 5), I discussed the determination of 
 the coefficients of expansion of air and of some other gases 
 between the fixed points of the thermometer and under pres- 
 sures little removed from that of the atmosphere. The various 
 methods of experimentation employed, speaking generally, show 
 one point in common: the expansions were not measured 
 directly, but were calculated from the changes in the tension. 
 In this second memoir I propose: 
 
 I. To complete the earlier researches and to study the rate 
 of expansion of gases between the same limits of temperature 
 but under very diverse pressures, by the use of analogous 
 methods, that is, those based upon the measurement of the 
 variations of the tension which a given volume of gas shows 
 when its temperature rises from to 100; 
 
 II. To examine the same subject in a direct way by an 
 entirely different method, in which we measure at once the 
 increase of volume which a rise of temperature from to 100 
 produces in a given quantity of gas subjected all the time to 
 the same pressure. 
 
 FIRST PART. 
 
 On the Rate of Expansion of Gases under Various Pressures, 
 
 Calculated from the Changes in the Tension. 
 Physicists generally assume that the rate of expansion of 
 gases is constant between the limits of temperature mentioned, 
 whatever the pressure to which the gases are subjected ; con- 
 sequently, that it is entirely independent of the original den- 
 sity of the gas. Yet it is difficult to cite any conclusive 
 experiments upon which this law may be based. Many observers 
 
 123 
 
MEMOIRS ON 
 
 have obtained the same figure for the coefficient of expansion 
 of air under various barometric pressures, and have from this 
 fact concluded that the coefficient of expansion of gases remains 
 constant under all pressures. Yet the barometric variations in 
 any given place are within limits too narrow to permit of draw- 
 ing so general a conclusion from such observations ; they only 
 prove that, for slight variations of pressure, the changes in the 
 coefficient of expansion of air are inappreciable. 
 
 H. Davy is the only physicist who has studied the expansi- 
 bility of gases under very varied pressures (Philosophical Trans- 
 actions, 1823, volume II, page 204). He states that he found 
 the expansion for air at the densities , J, , 1 and 2. Yet the 
 determinations were not made by a method exact enough for 
 us to consider their results as sufficiently accurate. 
 
 I have made experiments upon air under pressures much 
 lower than that of the atmosphere and, again, others under 
 pressures far greater. 
 
 Experiments under Pressures less than the ordinary 
 Barometric Pressure. 
 
 These determinations were carried out by Method IV 
 (Annales de Chimie, volume IV, page 38 [above, page 96] ), and 
 by means of the apparatus shown in Figs. 13 and 14 [page 96] ; 
 greater length, however, is given the tube /Yr/f about 770 
 millimeters from the tubulure H up to the mark a. After 
 placing the bulb in the vapor of boiling water and connecting 
 it, on the one hand, with the drying apparatus by means of the 
 side tube op and, on the other, with the tube FGH which is 
 cemented with mastic into its copper tubulure n, it is exhausted 
 a great many times, and the air allowed each time to enter 
 again very slowly : the tubes FH and //contain enough mer- 
 cury for a vacuum to be produced in the bulb without the 
 mercury rising above Fin the tube FH. When the apparatus 
 is completely dried out, the amount of air we wish to experi- 
 ment with is admitted ; its density being determined by the 
 difference of level of the two columns of mercury. The side 
 tube op is then sealed with a lamp and the drying apparatus 
 removed. 
 
 By pouring mercury into the tube //, the level in the tube 
 FH is adjusted at the mark a, -the bulb being all the 'time in 
 
 124 
 
EXPANSION OF GASES 
 
 the vapor of boiling water ; by means of the cathetometer the 
 difference of level of the two columns is read, and at the same 
 time the barometric height is recorded. 
 
 The furnace is then removed, the hot water in the vessel 
 Jfis drawn off and, when the latter has become quite cold, the 
 bulb A is surrounded with crushed ice. Mercury is drawn off 
 by opening the tap K so as to maintain the mercury level at 
 the point a in the tube FH. When temperature equilibrium 
 has once more been established, the difference of level of the 
 mercury columns is measured, as well as the barometric height. 
 
 Several determinations were thus made with the same speci- 
 men of air, having the bulb successively in the vapor of boil- 
 ing water and in melting ice. They were performed in some 
 cases after several days' interval ; in this way it was easy to 
 decide whether the apparatus was perfectly gas-tight. 
 
 I have brought together in a single table the determinations 
 made of the rate of expansion of air under pressures lower than 
 that of the atmosphere ; those that were made upon the same 
 specimen of air are comprised in a single series. 
 
 I used the same bulb as in my earlier experiments (volume 
 IV, page 42 [page 88, above] ), but the tube FH of the old 
 apparatus was replaced in Experiments II, III, IV, and V, by 
 another of greater height. 
 
 For Series I, we have 
 
 JL== 26.85_ OQ27 
 V 9889.9 ~ 
 and for Series II, III, IV and V, 
 
 V = 9889. 9 ==0 ' 00298 - 
 
 The formula which serves for the calculation of the experi- 
 ment is the following : 
 
 Representing by H 1 the barometric height at the time when 
 the experiment is carried out in [the vapor of] boiling water, 
 
 T the temperature of the vapor, 
 
 li l the difference of level of the mercury columns, 
 
 t l the temperature of the minute air-volume v, 
 
 H, h, t, the corresponding quantities when the experiment 
 is conducted in melting ice ; 
 
 We then have : 
 
 -*)- I t lH>-h>-H+h] 
 125 
 
MEMOIKS ON 
 
 We have assumed that t 1 = t. 
 
 The heights H, h, ff, li l have been reduced to by calcula- 
 tion. 
 
 In the calculation of the determinations the same figure for 
 melting ice has been combined with several results for boiling 
 water, made before and after, to eliminate the extreme values. 
 
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 3 to S5 -." fe Sj ^ 
 
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 ab 
 
EXPANSION OF GASES 
 
 This table shows clearly that the coefficient of expansion of 
 air continues to decrease with the pressure. 
 
 It is noteworthy that, in the several experiments made upon 
 the same specimen of air, greater variations are recorded than 
 in those made under atmospheric pressure. Thus, in Series V, 
 which comprises determinations made under very low pressures, 
 the extremes are 1.36376 and 1.36639 ; difference, 0.00263. 
 The reason for this is simple ; the same error made in the 
 reading of one of the heights H, H', h, or h', of necessity pro- 
 duces much more considerable variations in the final result, the 
 lower the pressures. It is only by a great many determinations 
 arranged so as to eliminate extreme figures, and by taking into 
 account all results that were obtained, that it has been possible 
 to prove the existence of the law stated above. 
 
 Experiments under Pressures greater than the ordinary 
 Barometric Pressure. 
 
 The apparatus [shown in] Volume IV, Fig. 13 and 14 [page 
 96] serves very well for experiments under pressures higher 
 than the atmospheric, when modified as follows: 
 
 The tube // is replaced by a much longer glass tube held 
 fast to a wall by numerous supports throughout its length. 
 Instead of the straight side tube op, there is cemented into the 
 tubulure o a tube of the form shown in Fig. 1 and consisting of 
 a bent capillary tube abc of which the portion ab is horizontal, 
 and of a larger tube cd sealed to the capillary tubing and verti- 
 cal in position. The latter connects with a large tube LL' 
 containing pumice stone moistened with concentrated sulphuric 
 acid: for this purpose, the ends of the two tubes are brought 
 together inside the little cover tube of copper which is then 
 covered all over with gum mastic. The tube LL' can be con- 
 nected by means of a rubber tube with a small air pump or 
 cemented into the tubulure t of a condensing pump. 
 
 A number of pellets of gum mastic are put in the tube cd. 
 
 This being arranged and the bulb being in the vapor of boil- 
 ing water, the apparatus is exhausted many times for the pur- 
 pose of drying it completely, then the vacuum pump is replaced 
 by the condensing pump; dry air is slowly forced into the bulb 
 
 127 
 
MEMOIRS OK 
 
 and, at the same time, mercury is poured into the tube IJ. 
 Some minutes are allowed to elapse between consecutive strokes 
 of the piston, in order to let the air remain some time in con- 
 tact with the sulphuric acid in the pumice stone before it 
 makes its way into the bulb. 1 When it is seen by the difference 
 
 FIG. 1. 
 
 FIG. 2. 
 
 of height of the mercury columns, that the air in the bulb is 
 at the desired density, the small pellets of gum mastic con- 
 tained in the tube cd are melted with the aid of an alcohol 
 lamp, and at the same time the tap K is opened a little; the 
 
 1 It is even more necessary in the case of determinations made under 
 high pressures than of those under low, that the air admitted to the 
 bulb should be perfectly dry. To secure this result to a certainty, care 
 is taken to fit a second tube of pumice stone and sulphuric acid to the 
 tubulure t' of the condensing: pump, so that the air introduced comes 
 iato the pump already well dried. 
 
 128 
 
EXPANSION OF GASES 
 
 mercury which runs out lowers the tension within enough to 
 cause a short column of melted gum mastic to make its way 
 into the capillary tube cb, where it solidifies. The same end is 
 manifestly reached by forcing in more air by means of the 
 condensing pump. The apparatus is now hermetically sealed 
 at c, when the gum mastic becomes cold; the tube LL and 
 the condensing pump can then be removed. 
 
 The determination proceeds as usual; only, since the col- 
 umns to be measured are very long, they cannot be brought 
 within the range of a single cathetometer. I have therefore 
 used in these experiments two eathetolneters at one time, each 
 of 1 meter's range. One of these instruments served to deter- 
 mine the distance of the meniscus in the tube FH down from 
 a mark r made upon the tube IJ at about 800 millimeters 
 above the mark a. The other cathetometer, fixed upon a very 
 steady base which the observer does not touch, serves to mea- 
 sure the distance from the meniscus in the tube // down to 
 another mark r' made upon this same tube. When the 
 distance rr is greater than 1 meter, other marks are put 
 upon the same tube in the interval, separated by about 900 
 millimeters. All these distances were each time determined 
 with the greatest care by means of cathometers, before the 
 experiment was begun and again after it was finished. 
 
 The meniscus, in the tube FH was adjusted in each experi- 
 ment approximately to coincide with the mark a on the tube: 
 since it is rather difficult to adjust such long columns of mer- 
 cury, I did not attempt each time to make the coincidence 
 perfect; I preferred to secure it only approximately and 
 to take account of the variation in the minute volume v, 
 from the position of the meniscus with respect to the 
 mark a, which was made easy by a previous calibration of the 
 tube. 
 
 The mercury column was protected from radiated heat by a 
 wall of several planks on top of one another: the tempera- 
 ture was determined by means of three thermometers with very 
 large bulbs, placed at different points along its length. The 
 mean of the readings of these thermometers was taken as the 
 temperature of the mercury column. 
 
 By means of the apparatus thus arranged I was able to 
 
 129 
 
MEMOIRS ON 
 
 make determinations up to a pressure of about four atmos- 
 pheres. The bulb was no longer that which had served for 
 the previous experiments; that was of too thin glass and 
 probably would- not have withstood so great a pressure. I 
 chose a thicker glass bulb and one of somewhat smaller diame- 
 ter; it held 6786.5 grams of mercury at 0. 
 
 In order to make observations at yet higher pressures, I was 
 compelled to resort to a new arrangement. I was unable to 
 procure glass tubing in single pieces of more than three meters 
 in length, and moreover I was afraid that a glass tube of 
 greater dimensions would not withstand the pressure and would 
 give way at the lower end. I had recourse to the following 
 apparatus (Fig. 1) [page 128]: 
 
 An iron tube, about three meters in length, is fitted into the 
 tubulure A of an iron vessel provided with a tap (Fig. 1, 2); 1 
 it is fastened in this tubulure by means of a packing of linen 
 greased with tallow, which is forced into the annular space 
 around the tube by means of the screw cap E. 
 
 In the second tubulure B is fixed in the same way the glass 
 tube FH. The iron vessel ABR is firmly fastened by a sup- 
 port 88' fixed upon a vertical wall. The iron tube is arranged 
 exactly vertical ; its upper end is made wider and is provided 
 with a screw-thread, and in this is fitted a glass tube about 2 
 meters in length with the aid of a packing of linen greased with 
 tallow and a screw cap. The iron tube and the glass tubing 
 which it carries have an interior diameter of 14 to 15 milli- 
 meters. 
 
 The bulb with the vessel that contains it is placed in a 
 neighboring room, separated from the first by the wall upon 
 which the vertical iron tube is fastened. This wall is pierced 
 with a hole through which the capillary tube of the bulb is 
 passed before it is cemented into the copper three-way tube 
 mno. The side tube mo carries a small bent tube abed contain- 
 ing pellets of gum-mastic, and is connected with the condens- 
 
 1 "Fig. 2 shows a vertical section of the vessel ABR on a scale double 
 that of Fig. 1. All the figures are -fa actual size, except Fig. 2 and 4 of 
 this memoir [see page 138] which are actual size. 
 
 130 
 
EXPANSION OF GASES 
 
 ing pump by means of the tube LL full of pumice stone 
 moistened with sulphuric acid. 
 
 The determination is in other respects carried out exactly as 
 with the former apparatus: the two menisci are followed with 
 two cathetometers. The instrument which follows the menis- 
 cus of the long column is placed on an upper floor, through the 
 planking of which the iron tube passes. 
 
 The tubes bear marks at chosen distances which have been 
 measured with the greatest care by means of one of the cathetom- 
 eters placed for this purpose upon high supports made as firm 
 as possible and upon which the observer doos not rest. The 
 very sensitive spirit level of the cathetometer, moreover, en- 
 ables one easily to judge if the condition of steadiness is satis- 
 factorily secured. 
 
 Mercury thermometers with large bulbs are arranged along 
 the mercury column and indicate its temperature. 
 
 The bulb used in these determinations was one of thick glass 
 which I had blown for me at the glass works of Choisy-le-Roi. 
 The walls of the bulb were about 3 millimeters thick and were 
 practically uniform throughout. The coefficient of expansion 
 of this bulb was determined from another smaller one, blown 
 at the same time, of the same material, and having almost the 
 same thickness of glass; it was found to be 0.002130 between 
 and 100. 1 
 
 The bulb used in the experiments on the rate of expansion 
 of gases held 5864.45 gr. of mercury at 0, apart from the 
 capillary stem. 
 
 Finally, there is a factor which we must know in order to be 
 able to calculate the rate of expansion of air from the results of 
 experiment: this is the increase in the capacity of the bulb 
 through the variation in the pressure upon the gas at and at 
 100. This variation would be difficult to determine perfectly 
 accurately, but it is easy to obtain an approximate figure. 
 
 To this end the bulb was filled with water to within a short dis- 
 tance from the end of the capillary stem, and this end was then 
 
 1 The data of this determination are the following: 
 
 P = 1265.647 gr. Hi = 763.50 mm. 
 
 p = 19.783 n=100.13 
 
 131 
 
MEMOIRS ON 
 
 cemented into a bent glass tube whose long vertical arm was 
 open. If it was desired to determine the changes of volume 
 for slight pressures, mercury was poured into the open end: 
 the air compressed in the other arm exerts pressure upon the 
 water surface in the capillary tube. The increase in the capac- 
 ity of the bulb is gauged by the movement of the water menis- 
 cus in the capillary tube, and the pressure by the difference of 
 level of the mercury columns. The bulb was immersed in a 
 vessel of water at the ordinary temperature, to render inappre- 
 ciable the volume-changes due to variations of temperature. 
 
 Below are some data obtained with the bulb which was used 
 in the determinations of page 56 [page 126] and in those of 
 the former memoir, page 42, volume IV [page 88] : 
 
 Under a pressure of The capacity increased by 
 
 227.7 mm. of mercury 0.000054 
 436.5 " 0.000103 
 
 687.8 " 0.000160 
 
 Evidently the capacity increases with the pressure; yet this 
 increase of volume is so slight that it may be completely neg- 
 lected in experiments made upon the expansibility of gases 
 under atmospheric pressure. The change in the capacity of 
 the bulb is actually still less than is here indicated, for in the 
 experiment described the apparent change was composed not 
 only of the increase in the volume of the glass bulb, but also 
 of the decrease in volume of the water; I have entirely neg- 
 lected the latter and have ascribed the whole change observed 
 to the variation in the bulb's capacity. 
 
 For studying the increase in the volume of the bulb under 
 higher pressures, I sealed a capillary tube of rather large bore 
 to a thick glass bulb similar to that of the experiments described 
 on page 61 [page 131]. This bulb was completely filled with 
 water and connected with a condensing pump and a small air- 
 manometer; in this way I obtained the following results: 
 
 Under an increase of The volume Under an increase of pressure 
 
 pressure of changed by of 1 meter [of mercury] 
 
 0.715 m. 0.0000740 0.0001035 
 
 1.814 0.0001940 0.0001069 
 
 3.035 0.0003288 0.0001083 
 
 4.178 0.0004538 0.0001086 
 
 132 
 
EXPANSION OF GASES 
 
 We shall assume 0.000108 [to be the increase produced] by 
 a rise in pressure of 1 m. of mercury. 
 
 To obtain the increase of the capacity of the bulb we must 
 subtract the amount the water is compressed for each meter's 
 pressure, that is, about 0.000064, according to MM. Colladon 
 and Sturm ; this yields 0.000044 for the expansion of the bulb 
 for an increase of pressure of 1 m. of mercury. 
 
 Thus to make the correction in our determinations, it will 
 suffice to add to the coefficient 6 T of the expansion of the 
 bulb by heat, the expansion produced by the rise of pressure, 
 
 which is 0.000044 g/ 
 
 In the above experiments the change in the capacity of the 
 bulb through an increase of pressure was determined at ordinary 
 temperature; yet it is really its value at the temperature of 
 100 that we need to know in order to allow for it in our 
 determinations of the rate of expansion of gases, and it 
 might be objected that at 100 this change would not be the 
 same. Yet it will be noted that this introduces a very minute 
 correction which may be neglected since, at most, it changes 
 the fourth decimal of the coefficient of expansion,, Thus it 
 may be assumed without inaccuracy that the compressibility of 
 glass is the same at 100 as at the ordinary temperature, 
 
 The formula in accordance with which the determinations 
 have been calculated is the following: 
 
 (ir + &') i+dr +0.000044 ' h ~ H -) 
 
 
 The following table contains the results obtained with these 
 two forms of apparatus. 
 
 133 
 
! 
 
 s 
 
 MEMOIRS OK 
 
 8 8 S 
 
 CO 
 
 co co co co 
 
 oo o o o o oo 
 
 CO ~* TH GO Oi ""* <N CD 
 
 CO CO t- T* CO CO CO CN 
 
 O5 ^^ ^ O TH ^H Oi 
 
 GO T-^ CO CO CN CO O 
 
 i-lr-l r-li-lTHiH <M(M 
 
 SSBS 
 
 O O O O 
 
 o o o 
 
 ^ ^ Tii ^41 
 
 1 
 
 * 
 
 O^ CDO^t-^ ^^T 
 
 CCD OiOiOO t~ t 
 
 -H -* Oi CO T-H t- 
 
 CD 00 O TH G^ T-H 
 
 CD eg t^ t^ oj qi 
 
 -<* CO O O CO CD 
 
 
 O O O O O O 
 
 y co t^ co co 
 
 Ci Oi Oi OS 
 QQ 
 
 t t- CO CO 
 
 - CO C 
 O O 
 
 S?SJ 
 
 CO lO O 3 
 
 CO T}< CO O 
 00 CO OO 00 
 
 8888 
 
 o c> o o 
 
 OO 00 1O CD P CO 
 
 lO O O O iO -^JH 
 
 CO CO CO CO 00 00 
 
 CO OO CD <N 
 
 <N <M" co co 
 
 Q 
 
 : 
 
 B t- 
 
 < CD f 
 
 CO ^ ^ 
 
 SOS GO 
 . . ^ 
 
 t- t- t- t- 
 
 134 
 
 (>l C^ O1 CO 
 
 o: os os os 
 
 t t- t t- 
 
EXPANSION OF GASES 
 
 This Table shows that the coefficient of expansion of dry 
 air increases in a marked way with the pressure, and conse- 
 quently confirms the result already reached by the determina- 
 tions, page 56 [page 126], made under pressures lower than 
 that of the atmosphere. 
 
 Summing up, we have found the following figures for the 
 value of the coefficient of expansion of air under various pres- 
 sures : 
 
 Pressure at 0. 
 
 Pressure at 100 
 
 Density of air at 
 0, that of air at 
 under a pressure of 
 760 mm. being 
 taken as unity. 
 
 1 + 100 a 
 
 109.72 
 
 149.31 
 
 0.1444 
 
 1.36482 
 
 174.36 
 
 237.17 
 
 0.2294 
 
 1.36513 
 
 266.06 
 
 395.07 
 
 0.3501 
 
 1.36542 
 
 374.67 
 
 510.35 
 
 0.4930 
 
 1.36587 
 
 375.23 
 760.00 
 
 510.97 
 
 0.4937 
 1.0000 
 
 1.36572 
 1.36650 
 
 1678.40 
 
 2286.09 
 
 2.2084 
 
 1.36760 
 
 1692.53 
 
 2306.23 
 
 2.2270 
 
 1.36800 
 
 2144.18 
 
 2924.04 
 
 2.8213 
 
 1.36894 
 
 3655.56 
 
 4992.09 
 
 4.8100 
 
 1.37091 
 
 The third column of the table comprises the densities of the 
 gas at the temperature of melting ice ; it will be seen that 
 these vary from 0.1444 up to 4.8100, that is, from 1 to 33.3, 
 and for so great a change in density, the coefficient of expan- 
 sion of the gas changes only from 0.3648 to 0.3709. 
 
 The above determinations therefore prove that the law 
 assumed correct by physicists, viz., that air expands [on heat- 
 ing] the same fraction of its volume at 0, whatever its density, 
 is not accurate ; air expands, between the same temperature- 
 limits, by amounts which are greater in proportion as the 
 density of the gas is higher, or, in other words, as the mole- 
 cules are closer together. 
 
 Similar determinations were made with carbonic acid gas by 
 means of the two pieces of apparatus described : they gave the 
 following results : 
 
 135 
 
MEMOIRS ON 
 
 Apparatus I. 
 
 Apparatus II. 
 
 JET 
 
 ..759.94mm. 
 
 760.03 mm. 
 
 t 
 
 . 145 
 
 13.9 
 
 h 
 
 ...982.75 mm 
 
 982.74 mm. 
 
 V 
 
 0.00361 
 
 0.00362 
 
 V 
 
 
 
 H+h... 
 
 .1742.69mm. 
 
 1742.77 mm. 
 
 H' 
 
 ..759.86 
 
 759.83 
 
 T' 
 
 ..100.0 
 
 99.99 
 
 ' 
 
 . . . 15 8 
 
 15.6 
 
 h' 
 
 .1627.81 mm. 
 
 1627.95 mm. 
 
 H'+h' . 
 
 .2387.67 
 
 2387.78 
 
 v< 
 
 ....0.00366 
 
 0.00367 
 
 V 
 
 
 
 1+lOOa. 
 
 ...1.37520 
 
 1.37525 
 
 757.69 mm. 757.79 mm. 
 
 11.3 11.2 
 
 2831.37mm. 2831.19 mm. 
 0.00190 0.00190 
 
 3589.06 mm. 3588.98 mm. 
 
 758.11 758.41 
 
 99.93 99.94 
 
 11.3 11.4 
 
 4200.50 mm. 4201.05 mm. 
 
 4958.61 4959.46 
 
 0.00190 0.00190 
 
 1.38586 
 
 1.38609 
 
 Combining these results with those given in the earlier 
 memoir, volume IV, pages 57 and 60 [ pages 109 and 113], we 
 have for carbonic acid gas : 
 
 Pressure at 0. 
 
 Pressure at 100. 
 
 Density of the 
 gas at 0. 
 
 1 + lOOa 
 
 758.47 m m. 
 
 1034.54 m m. 
 
 1.0000 
 
 1.36856 
 
 901.09 
 
 1230.37 
 
 1.1879 
 
 1.36943 
 
 1742.73 
 
 2387.72 
 
 2.2976 
 
 1.37523 
 
 3589.07 
 
 4759.03 
 
 4.7318 
 
 1.38598 
 
 It is evident that the rate of expansion of carbonic acid gas 
 increases more rapidly with the pressure than does that of 
 atmospheric air. 
 
 SECOND PART. 
 
 Experiments to determine the Rate of Expansion of 
 Gases under Constant Pressure. 
 
 In all the experiments described up to the present the rate 
 of expansion of the gas has been determined indirectly. We 
 measure directly the increase in the tension which the gas, 
 maintained at a constant volume, exerts by reason of the rise 
 in temperature, and from this we calculate the rate of expan- 
 sion on the basis of Mariotte's. Law. Yet it may be objected 
 that it has not been shown that this law is absolutely exact 
 even for air, and, consequently, that the increments deter- 
 mined in the rates of expansion under different pressures may 
 
 136 
 
EXPANSION OF GASES 
 
 only point to the fact that Mariotte's Law is not rigorously 
 true. 
 
 This objection does not seem to me to be justified, for sev- 
 eral reasons. As a matter of fact Dulong and Arago did not in 
 their brilliant research discover any constant variation even at 
 pressures as high as 27 atmospheres, which in any case shows 
 that, between the limits of pressure of 1 and 27 atmospheres, 
 Mariotte's Law is practically exact ; hence we may conclude 
 that it would be rigorously accurate for differences of pressure 
 as small as those observed in our researches on any given gas, 
 at and at 100. It is clear that, were there a variation 
 which such small differences of pressure could render evident 
 in measurements of the rate of expansion, this variation would 
 certainly be revealed in a very marked degree by the great dif- 
 ferences of pressure in determinations made with as much care 
 as those of the distinguished physicists I have named. 
 
 I should state, too, that my experiments were carried out 
 under precisely those conditions which would be most favor- 
 able for exactness in Mariotte's Law, since it is the gas heated 
 to the temperature of 100 consequently, at the very time 
 when it is farthest removed from its condensation point that 
 it is subjected to the greatest pressure. 
 
 Finally, it should be noted that, in the parallel determina- 
 tions made upon the compressibility of different gases under 
 one and the same pressure, it was shown that the gases which 
 do not follow Mariotte's Law show a greater diminution of 
 volume than should take place according to the Law. There- 
 fore in my experiments, neglecting the changes occurring in the 
 molecular forces on account of the difference in temperature, 
 the volume of the gas at 100 ought to be smaller than what 
 exactly accords with Mariotte's Law ; so that the variation in 
 Mariotte's Law would tend to diminish the coefficient of expan- 
 sion with [increase of] the pressure, instead of increasing it as 
 we have found in our experiments. 
 
 After all, to avoid leaving any doubt upon this important 
 point in the dynamical theory of gases, I made a new series of 
 determinations by a method in which the increase in the vol- 
 ume of the gas is measured directly, while it remains under 
 practically the same pressure at and at 100. This method 
 J 137 
 
MEMOIRS ON 
 
 is clearly the only one that can be used with gases which do 
 not follow Mariotte's Law for slight changes of pressure. 
 
 I shall describe briefly the apparatus I have used in these 
 determinations and which is based upon the same principle as 
 that used by M. Pouillet in his air pyrometer. It is shown in 
 Fig. 3. 
 
 Z 
 
 FIG. 3. 
 
 A glass bulb sealed to a capillary tube is placed in a tin-plate 
 vessel MN (Fig. 13, Volume IV) [page 96]. The tube is 
 cemented into the little three-way tube mno. In the side- 
 tubulure o is cemented a short straight piece of capillary tub- 
 ing, or else a tube of the shape of abed, Fig. 1, Volume V [page 
 128], and containing some pellets of gum mastic, according as 
 we must work under pressures lower or higher than that of the 
 atmosphere. Into the third tubulure n is cemented the bent 
 capillary tube EF connecting with the tube FH in which the 
 increase of volume of the air is measured. The latter is so 
 chosen that the quantity of air which fills it to a when the bulb 
 
 138 
 
EXPANSION OF GASES 
 
 is in melting ice, occupies, when the bulb is in [the vapor of] 
 boiling water, most of the space down to a mark p made upon 
 the narrower tube below. The tube FH is cemented with 
 mastic into the tubulure A of an iron support provided with 
 taps. Into the second tubulure B is cemented a glass tube BI, 
 a meter long in experiments made under atmospheric pressure. 
 This tube was replaced by one of 3 meters' length when work- 
 ing with greater pressures. 
 
 The iron support has two taps R and R'. The first tap R is 
 traversed by a single hole and serves to draw off a part of the 
 mercury contained in the apparatus. The second tap R 
 is bored with two holes at right angles to each other, and 
 serves to connect the tube FH, according to the position given 
 it, with the barometric tube BI, or directly with the outside. 
 This arrangement is clearly seen in Fig, 4 [page 138], which 
 represents a vertical section of the support and the two posi- 
 tions (a) and (&) of the tap R. This support is fastened to a 
 cast tripod provided with levelling screws, upon which is fitted 
 a glass jacket filled with water for keeping the expansion reser- 
 voir at a known temperature. This jacket consists of a rect- 
 angular box two of whose opposite sides are made of glass. 
 
 The experiment is then made as follows : 
 
 The bulb being surrounded with melting ice, the tube op open 
 and connected with the apparatus which was used before to dry 
 the air, mercury is poured into the tube BI until it reaches the 
 level of a. The tap R being in position (a), the mercury of 
 course rises to the same level in the two communicating tubes. 
 The tube op is closed by means of a lamp, [the height of] the 
 barometer is recorded, as is also the temperature of the water 
 in the jacket, which has been carefully stirred from time to 
 time by means of the stirrer ffgg' which is moved up and down 
 in a vertical plane so as to make it pass through all strata of 
 the liquid. 
 
 After removing the ice, the water in the vessel M is brought 
 to boiling. To keep the two columns of mercury at about the 
 same point, it becomes necessary to draw off mercury by open- 
 ing the tap R. A part of the air in the bulb thus passes into 
 the tube FH; the two columns are brought approximately to 
 the same level 0, and the difference of height is determined 
 
 139 
 
MEMOIES ON 
 
 accurately by means of the cathetometer; l at the same time the 
 [height of the] barometer and the temperature of the jacket 
 are recorded. The water filling the jacket was continuously 
 stirred for at least a quarter of an hour before beginning the 
 observations, to give it a uniform temperature which would at 
 the same time be that of the air enclosed in the tube FH. 
 
 To be able from this experiment to calculate the coefficient 
 of expansion of air, we must know the capacity of the bulb, the 
 volume v from E to a of the air in the tube FH when the bulb 
 is in melting ice, and the volume v' from E to p which is filled 
 by air when the bulb is in [the vapor of] boiling water. The 
 first is easily found by filling the bulb with mercury at 0, 
 after having made it boil for a while in the apparatus. (See 
 volume IV, page 22 [page 82].) 
 
 The two volumes v and v' are determined in the following 
 way: 
 
 The drawn-out end of the tube op is broken off to allow com- 
 munication between the interior and the outside air, 2 and mer- 
 cury is poured into the tube BI until this liquid entirely fills 
 the tube FH as far as y on the capillary tube. The tap R' is 
 turned into the position (#). There is then no connection 
 between the tubes FH and BI, but the mercury from FH flows 
 out by the opening 0'. This mercury is caught in a flask. 
 Mercury is allowed to run out until the meniscus comes exactly 
 
 1 There was danger lest the jacket full of water would give rise, on 
 account of refraction, to deviations of the rays which come from the 
 menisci : a very simple test showed me there was no appreciable devia- 
 tion, at any rate in the places where the readings were made. The tube 
 op being open, the mercury meniscus was adjusted at points all along 
 the tube FH in succession. It was seen, with the aid of the glass of the 
 cathetometer, that in all these positions the menisci were at the same 
 level in the two tubes FH and BI. 
 
 a To prevent the entrance of moist air into the apparatus, care is 
 taken first to connect the tube op with the drying apparatus by means 
 of a rubber tube. In many experiments, chiefly those made upon gases 
 other than atmospheric air, the point of the tube op is not broken off. 
 The bulb being in the [vapor of 1 boiling water, mercury is poured into 
 the tube BI so that the liquid rises into the capillary part EF of the 
 tube FH', the volumes v and v' are then calibrated as usual. 
 
 140 
 
EXPANSION OF GASES 
 
 to the position at a that it had in the first part of the experi- 
 ment: this is done with great precision with the aid of the glass 
 of the cathetometer. 1 The mercury which has flowed out is 
 weighed, and from this the volume v is calculated. 
 
 The mercury is then run out until the meniscus coincides 
 with p. The weight of mercury drawn off, added to that which 
 gave the volume v, will give us the volume v'. It is clear there 
 is a correction to be made on account of the temperature; if p 
 and p' represent the weights of mercury drawn off and t the 
 temperature of the water of the jacket at the time of the cali- 
 bration, the weights of mercury at which will occupy the 
 volumes v and v', and which, consequently, actually represent 
 
 these volumes, are p (1 + i-) and^r (1 + ~)> 
 
 It is necessary to add to these volumes v and v' the small 
 volume of the capillary tubing outside the vessel in which the 
 water is boiling. This volume was determined by a preliminary 
 calibration. On the other hand, since the temperature of the 
 air contained in these tubes is somewhat uncertain, it is desir- 
 able that this volume should be extremely small. In my appa- 
 ratus it never exceeded ^^^ of the capacity of the bulb. 
 
 In order to adapt the same apparatus for measuring the rate 
 of expansion of air under high pressures, the lateral tube op is 
 replaced by the twice-bent tube abed of Fig. 1 [page 128], and 
 dry air is forced into the bulb, while mercury is poured into the 
 tube BI. When the desired pressure has been got in the bulb, 
 the gum mastic in the tube abed is melted so as to close the 
 apparatus hermetically ; the bulb is surrounded with melting 
 ice and the meniscus is adjusted to the mark a with the aid of 
 a cathetometer. The meniscus in the tube BI is brought in 
 line with a second cathetometer. In these measurements the 
 precautions noted on page 59 [page 129] are followed closely. 
 
 After removing the ice, the water in the vessel is raised to 
 boiling, and mercury is drawn off so as to make the level coin- 
 cide with 0. 
 
 The height of the raised column of mercury is measured ; it 
 
 1 The flow of the mercury is made as slow as may be desired by turn- 
 ing the tap to the proper extent: it is easy to adjust the meniscus in 
 this way within about -fa of a millimeter. 
 
 141 
 
MEM OIKS ON 
 
 is practically the same as that of the first part of the determi- 
 nation. 
 
 If Hand H' represent the barometric heights at the time of 
 the readings for [the temperatures of] melting ice and boiling 
 water, and h and h' the differences of level of the menisci in 
 the tubes of the apparatus, we evidently have the equation 
 
 hence 
 
 (H' + h') (1 + 6 T) 
 
 V 1 + at 
 
 The quantity a enters into the denominator of the second 
 member ; but as it affects the result only slightly, we make use 
 of the method of successive approximations, that is, an 
 approximate value is given , from this the value of a in the 
 first member is calculated and this is then substituted in 
 the second member and yields t'he final value of 1 + a T. 
 
 In this method the greatest care must be exercised in the 
 determination of the volumes F, v and v', and, even more, in 
 the determination of the temperature t'. There is, finally, 
 another very important matter the perfect drying of the tube 
 FH. This tube has a large capacity and, on account of the 
 arrangement of the apparatus, cannot be heated while it is 
 exhausted. In my experiments this tube was thoroughly dried 
 at a high temperature before being cemented into its tubulure, 
 and, when the apparatus was completely set up, a little mercury 
 was poured into the communicating tubes; the tap R was 
 turned to a position intermediate between (a) and (#), and the 
 apparatus exhausted, the bulb being surrounded by the vapor 
 of boiling water. By exhausting a great many times and then 
 allowing dry air to enter slowly, the moisture should not only 
 be completely removed from the bulb but also from the tube in 
 which the expansion is measured. 
 
 The table below contains the results obtained in the experi- 
 ments made by this method, at atmospheric pressure, upon air, 
 hydrogen, carbonic acid gas, protoxide of nitrogen, oxide of 
 carbon, sulphurous acid gas, and cyanogen. 
 
 The second part of the table contains [the results of] experi- 
 
 142 
 
EXPANSION OF GASES 
 
 meuts made upon atmospheric air, hydrogen, and carbonic acid 
 gas under higher pressures. 
 
 eocococococoeooocoeococo 
 
 8 81 8 $ g 8 3 S S 8 S $ $ 8 8 S 8 8 8 So 
 
 oOOOOJ^C^C^C^O'T^T-Hi i'r-icd'rfC7COQO l T:PiO 
 
 g.g-i c $88 8.ii.g g 3 S B e B83 g 
 
 cococopQOi-iostocoi.-ooiooOi-ciot-ooO'g'O 
 
 g i g g i' g g g g i i i i i i i i i i i i 
 
 g 8 8 g 5 $ SSSSSSfegggg 
 
 -* 1-1 <N o o CM' o o o o o i- c* o. o* oi oi o o o o 
 
 S I I I I I I I I I I + + + + + 
 
 8 8 g fc 8 g ^ S g 
 
 8 8 8 S g S S 
 
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 J _." -* SV ^-- <_ 03 O S^) TT 10 O 
 
 2SSSSSS55S 5 SSS^SS5SSti 
 
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 050505S050J05055S5S OTWOsSjOJOCftol 
 
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 ^ I I i i g* i i i i i i i i i i i i i i i i g g ^ I 
 
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 S? S S S 5 
 
 * o * i> od od p t^ i^ od os' oi in os od co 06 
 
 THT-lT-(THT-(-rH5iT-l-I-lT-lT-lT-l->-ll-ll-lT-l1-l 
 
 -(l-^-^CO^iOAOiOCOCOCOiOiO^fT^CpTfOS 
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 w t- I- I- I- t- t^- t- C- t- t- I- t- I- l> t- t>- l^- 
 
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 3 ** ti f- 
 
 143 
 
MEMOIRS ON 
 
 Atmospheric air gives figures a little higher than the mean 
 of earlier determinations; yet the difference is inappreciable; it 
 may be attributed also to the fact that air does not conform 
 rigorously to Mariotte's Law. 
 
 My earlier determinations gave for hydrogen the same 
 coefficient of expansion as for air. The new experiments 
 assign to hydrogen a coefficient slightly lower than that of air. 
 Hr. Magnus has already reached a similar result (Annales de 
 Chimie et de Physique, volume IV, page 334), but the differ- 
 ences are so small that it is difficult to decide the question; they 
 are within the limits of the errors of observation. As a matter 
 of fact, there are in Magnus' determinations with air many 
 figures which are still lower than those he has found for hydro- 
 gen; so that the question does not seem to me settled. It will 
 be seen later that the experiments made upon the rate of 
 expansion under higher pressures decide the matter in a very 
 clear way. 
 
 The hydrogen was prepared from very pure zinc; it was 
 passed through a wash bottle containing water, two tubes a 
 meter long full of pumice-stone soaked with a concentrated 
 solution of potash, a tube of equal length full of pumice stone 
 soaked with a solution of silver sulphate. Beyond the air 
 pump it traversed two tubes a meter long full of pumice stone 
 soaked with concentrated sulphuric acid, and a tube filled with 
 small bits of caustic potash. The latter was to hold back the 
 small quantity of sulphurous acid gas which might be formed 
 through the interaction of the hydrogen gas and the sulphuric 
 acid. This precaution had been neglected in the determina- 
 tions of the first memoir, yet I have never perceived any odor 
 from the presence of sulphurous acid in any of these experi- 
 ments. 
 
 Oxide of carbon gave the same figure as in the earlier 
 researches (volume IV, page 52 [page 109] ). 
 
 The coefficients of expansion of carbonic acid gas and pro- 
 toxide of nitrogen determined by this method are higher than 
 those obtained by the earlier methods (volume IV, pages 52, 56 
 and 57 [pages 109, 113, 115] ); this is unquestionably due to the 
 fact that these gases do not exactly conform to Mariotte's Law, 
 and that their volumes at 100, under a pressure higher than 
 
 144 
 
EXPANSION OF GASES 
 
 that to which they are subjected at this temperature in the 
 earlier methods, are smaller than they ought to be according 
 to this Law. We must expect to find similar results with all 
 gases more compressible than air. 
 
 The coefficients of expansion of sulphurous acid [gas] and 
 cyanogen are much higher than those of other gases. My 
 earlier researches (volume IV, pages 52 and 57 [pages 109 and 
 114] ) had, on the other hand, assigned them figures very little 
 higher than the coefficient of expansion of atmospheric air. 
 The variations may be attributed to the fact that, sulphurous 
 [acid] gas and cyanogen being much more compressible than 
 air, their volume at 100, calculated from the change of ten- 
 sion, is much too low and, consequently, gives too small a 
 coefficient of expansion. In an endeavor to verify this sup- 
 position by means of direct experiments, and after many trials, 
 I found that there had been a serious error in my former 
 determinations of sulphurous acid [gas] and cyanogen. 
 
 I have always had to face the difficulty of drying sulphurous 
 acid gas completely, the presence of a trace of moisture being 
 able, in the case of this very soluble gas, to cause much greater 
 variations than in other gases. My earliest experiments had 
 given for sulphurous acid [gas] figures much higher than those 
 to which I was led in my former research; but I discovered that 
 these figures became lower in proportion as the gas was more 
 slowly admitted into the bulb, which I most naturally attrib- 
 uted to more perfect drying, and it was only by having the 
 gas enter extremely slowly, compelling it to remain for a long 
 time in the tubes full of pumice stone soaked with concen- 
 trated sulphuric acid before introducing it into the bulb, that 
 I succeeded in securing constant figures. Working in this 
 way, a source of error is introduced which then escaped me; 
 some dry air evidently entered the bulb along with the sulphur- 
 ous acid gas. The proportion of this air was greater, the 
 slower the introduction of the sulphurous acid gas. Now the 
 presence of a small amount of air is sufficient to lower appreci- 
 ably the coefficient of expansion of sulphurous acid [gas], since 
 the latter gas expands under these circumstances as if it were 
 under a very low pressure, and the coefficient of expansion of 
 sulphurous acid [gas] falls very rapidly with the pressure, 
 
 145 
 
MEMOIKS ON 
 
 I thought at that time that the entrance of air must be due 
 to the fact that the apparatus (perhaps the taps of the pump 
 through the action of the acid gas) had not remained gas-tight 
 during the long time the gas was making its way in. I am not 
 prepared to assert this was not the case, yet 1 can say that the 
 apparatus was always tested with great care each time before 
 commencing a series of experiments with any particular 
 gas. 
 
 Yet there is another source of error against which I was not 
 sufficiently on my guard in my earlier experiments. It lay in 
 the great difficulty met with in freeing the pumice stone and 
 sulphuric acid from air mechanically held or absorbed; thus, I 
 found, in the experiments with sulphurous acid [gas], that 
 after the apparatus had been exhausted three or four times in 
 succession, at least to 1 or 2 centimeters, and sulphurous acid 
 gas had been introduced each time, the gas in the bulb still 
 showed on testing an appreciable amount of air mixed in. In 
 the ordinary determinations with gases other than atmospheric 
 air, I was accustomed to exhaust at least ten or twelve times; 
 in the experiments with sulphurous acid gas I contented myself 
 with only three or four times, because of the very long time 
 required for each filling. In the experiments with cyanogen, 
 only two exhaustions were made, on account of the difficulty of 
 preparing a considerable quantity of this gas in a pure state. 
 
 Sulphurous acid gas in the recent determinations was pre- 
 pared by the action of mercury upon sulphuric acid; the gas 
 passed through a long inclined U-tube full of concentrated sul- 
 phuric acid which the bubbles traversed very slowly; from this 
 it made its way to the bulb through a tube connecting with the 
 small air pump. This arrangement permitted the exhaustion, 
 not only of the receiving bulb, but also of the generating appa- 
 ratus. Besides, it was easy to prove, by means of the com- 
 municating tubes .PIT and BI, that the apparatus was perfectly 
 gas tight. 
 
 The bulb had in this way been filled with perfectly pure sul- 
 phurous acid gas. I satisfied myself after the determinations 
 were over, by breaking off the tip of the tube op under mer- 
 cury and driving out part of the gas by pouring mercury into 
 
 146 
 
EXPANSION OF GASES 
 
 the tube BI. The gas was completely absorbed by a solution of 
 potash.i 
 
 A similar arrangement was used in the work on cyanogen. 
 This gas was prepared by decomposing cyanide of mercury with 
 the aid of heat; it passed through a long column of concen- 
 trated sulphuric acid. 
 
 If we adopt the figures found for the coefficients of expansion 
 of the various gases by this last method, which is the only one 
 capable of giving comparable results when we wish to know the 
 rates of expansion of gases which do not follow Mariotte's Law, 
 it is apparent that the various gases show very different co- 
 efficients of expansion. We have found, as a matter of fact, for 
 these coefficients: 
 
 Hydrogen 0.36613 
 
 Atmospheric Air 0.36706 
 
 Oxide of Carbon 0.36688 
 
 Carbonic Acid Gas 0.37099 
 
 Protoxide of Nitrogen 0.37195 
 
 Cyanogen 0.38767 
 
 Sulphurous Acid Gas 0.39028 
 
 I have already shown above that the coefficients of expansion 
 of carbonic acid gas and protoxide of nitrogen were higher 
 when determined by the last method than when calculated from 
 the changes in tension. The variations are much greater for 
 the very compressible gases, such as cyanogen and sulphurous 
 acid gas, as may be understood from the following results, 
 which have been reached in the same series of determinations 
 as the figures given in the table above. As a matter of fact, in 
 order to obtain, with the apparatus of Fig. 3 [page 138], the 
 variations of tension in the gas occupying a constant volume, 
 when it is carried from the temperature of melting ice to that 
 of boiling water, it is only necessary to keep the level of the 
 mercury at a in the tube FH while the bulb is in [the vapor of] 
 boiling water, and to measure the difference of level between a 
 
 1 It remains to be decided whether sulphurous acid gas is completely 
 dried by concentrated sulphuric acid, and whether it did not carry with 
 it a minute quantity of the latter acid. This point seemed to be hard 
 to decide by direct experiment; the coefficient of expansion of the gas 
 is perhaps appreciably changed by the presence of an infinitesimal 
 quantity of [water] vapor. 
 
 147 
 
MEMOIRS ON 
 
 and the meniscus of the mercury pushed up in the tube BL 
 These determinations were made, in fact, in the three experi- 
 ments upon gaseous sulphurous acid and in the two experiments 
 upon cyanogen. With the values for H, t, h, v, and H+h of 
 the table above [page 143] it is only necessary to combine the 
 following: 
 
 Sulphurous Acid Gas 
 
 Cyanogen 
 
 II 
 
 III 
 
 H' 
 
 759 31 mm 
 
 760.71 mm. 
 
 762.13 mm. 
 
 T 1 
 
 99.98 
 
 100.03 
 
 lOO.OSo 
 
 f 
 
 19.29 
 
 19.88 
 
 18.42o 
 
 h' 
 
 ..288.62mm. 
 
 286.19mm. 
 
 284.30 mm. 
 
 H' + ft'. 1047.93 mm. 1046.90 mm. 1046.43 mm. 
 
 v' 21.44 gr. 25.79 gr. 28.20 gr. 
 
 1 + 100 a.. 1.38439 1.38451 1.38470 
 
 Thus, we have found: 
 
 I II 
 
 763.07 mm. 764.07 mm. 
 
 100.12 100.15 
 
 20.94 19.16 
 
 289.23 mm. 287.62 mm. 
 
 1052.30mm. 1051.69 mm. 
 
 22.80 gr. 25.62gr. 
 
 1.38282 1.38298 
 
 For Sulphurous Acid Gas: 
 By direct measurement of expansion. 
 
 0.39094 
 
 0.38987 
 0.39004 
 
 By calculation, from the change 
 of tension. 
 0.38439 
 0.38451 
 0.38470 
 
 Mean 0.39028 
 
 0.38766 
 0.38768 
 
 For Cyanogen: 
 
 0.38453 : 
 
 0.38282 
 0.38298 
 
 0.38290 
 
 Mean 0.38767 
 
 I have stated above that the coefficient of expansion of sul- 
 phurous acid gas rises quite rapidly with the pressure; this may 
 be observed in the following experiment, begun by filling the 
 bulb, while cooled with ice, and the expansion-tube FIf down to 
 /?, with sulphurous acid gas. The tube op was then sealed 
 with the lamp and, by pouring mercury into the tube BI, the 
 gas contained in the tube FH was forced back into the bulb. 
 
 1 This figure differs little from the mean assumed by Hr. Magnus, but 
 from three determinations which gave too divergent figures, viz., 
 0.3897; 0.3839; 0.3832. 
 
 148 
 
EXPANSION OF GASES 
 
 In other respects the determination is carried out as has 
 been described in volume IV, page 43 [page 99] ; we have : 
 
 H = 761.33 mm. H' = 761.08 mm. 
 
 = 18.83 T = 100.04 
 
 h = 221 .40 mm. t' = 19.10 
 
 v = 25.36 gr. h'= 226.56 mm. 
 
 H-\- h = 982.73 mm. H' + h' = 987.64 mm. 
 
 v ' = 1780.44 gr. 
 1+ ; 00 a= 1.39804. 
 
 Thus, for a change in pressure as slight as that from 760 mm. 
 to 980 mm., the coefficient of expansion of sulphurous acid 
 [gas] has changed from 0.3902 to 0.3980, and the gas under 
 the pressure of 980 mm. is not even at near its point of con- 
 densation. 
 
 It is likely, judging from this, that vapors have coefficients 
 of expansion very different from that of air at points slightly 
 removed from their points of condensation consequently, 
 under the conditions where we usually meet them in our exper- 
 iments for determining their densities. 
 
 Let us now turn to the second part of the table [page 143] 
 which contains determinations made under a pressure of 
 2530 mm. (about 3.33 atmos.) with three gases, atmospheric air, 
 hydrogen, and carbonic acid gas. The very striking fact is 
 there apparent that hydrogen has maintained practically the 
 same coefficient of expansion as under atmospheric pressure ; 
 whereas air, and, above all, carbonic acid gas show a very 
 marked increase in their coefficients. 
 
 The variation in rates of expansion of atmospheric air and 
 carbonic acid gas is far more noteworthy in those experiments 
 where the pressure is the same at and at 100, than in those 
 where the rates of expansion were calculated from the change 
 of tension. 
 
 At the same time it is clear that in proportion as the pres- 
 sure under which the gases are studied is greater, so much the 
 more marked become the variations among their coefficients of 
 expansion. Hydrogen and atmospheric air, which have prac- 
 tically the same rate of expansion under ordinary barometric 
 pressure, show very marked differences when they are subjected 
 to pressures three or four times as great. 
 
 149 
 
MEM OIKS ON EXPANSION OF GASES 
 
 Conclusions. 
 
 To sum up, my determinations do not confirm the two fun- 
 damental laws of the theory of gases, assumed up to the present 
 by all physicists to be exact, viz. : 
 
 I. All gases expand to the same extent between the same 
 limits of temperature. 
 
 II. The rate of expansion of a given gas, between the same 
 limits of temperature, is independent of its original density. 
 
 Must these laws be banished from science for the future ? I 
 do riot think so. I believe that these laws, along with all those 
 which have been discovered for gases, such as the Law of Vol- 
 umes, etc., are true at the limit, that is, that they come nearer 
 to conforming with the results of observation in proportion as 
 we use the gas in a more expanded condition. 
 
 These laws hold good for a perfect gaseous state, which the 
 gases that nature places before us, more or less approach, ac- 
 cording to their chemical characteristics ; according to the 
 temperature at which we study them and which may be, for 
 each in turn, more or less removed from the point where 
 change of state takes place ; finally and chiefly, according to 
 their condition of less or greater compression. 
 
 150 
 
RESEARCHES UPON THE GAS THERMOMETER, 
 
 AND THE COMPARISON OF THE GAS THERMOMETER, 
 
 WITH THE MERCURY THERMOMETER. 
 
 BY P. CHAPPUIS. 
 
 (Abstract) 
 
 Travaux et Memoires du Bureau International des Poids et 
 Mesures, volume 6 (1888); Archives des Sciences (Geneve), vol- 
 ume 20, pages 536, 153179, 248262 (1888). 
 
 151 
 
CONTENTS. 
 
 PAGE 
 
 Gas reservoir and baths . . 153 
 
 Manometer v . . . 1** 
 
 Barometer .... 155 
 
 Mercury Thermometers , ... . . 155 
 
 Average Coefficient of Expansion of Nitrogen, 100 . 156 
 
 ditto Carbon dioxide, ditto . 157 
 
 ditto Hydrogen, ditto . 157 
 
 Curves showing deviations from Mercury thermometers . 158 
 
 Coefficients of Expansion of Nitrogen and Carbon dioxide 
 
 at various temperatures between W and 100 . . 158 
 
 152 
 
RESEARCHES UPON THE GAS THERMOMETER, 
 
 AND THE COMPARISON OF THE GAS THERMOMETER 
 
 WITH THE MERCURY THERMOMETER. 
 
 BY P. CHAPPUIS. 
 
 (Abstract.) 
 
 IN an extended memoir Chappuis describes the means he em- 
 ployed in his attempt to determine with greater accuracy than 
 had hitherto been attained, the relation existing between the 
 rates of expansion of gases and of mercury. In the effort to 
 find an instrument which would be more reliable than the air 
 thermometer of Regmiult, he made use of a gas reservoir the 
 material of which was an alloy of platinum and iridium instead 
 of glass, and thereby avoided, in part at least, the difficulties 
 introduced through the uneven expansion of the latter sub- 
 stance. This reservoir was 110 centimeters long, 3.6 centi- 
 meters in diameter and had a capacity of a little more than a 
 litre. It was connected by means of a platinum capillary 
 tube a meter long with the manometric apparatus. For ex- 
 periments at C. and below, as well as at temperatures up to 
 50, the gas reservoir was supported in a horizontal position in 
 the inner one of two concentric metal troughs, and the mer- 
 cury thermometers were disposed symmetrically about it. In 
 this position it could be surrounded with crushed ice, with 
 freezing-mixtures or with liquid baths of any desired tempera- 
 ture ; in the last case stirrers driven by a water motor kept the 
 liquid in motion and at a perfectly uniform temperature. 
 Evaporation with consequent temperature-variation was largely 
 avoided by covering the troughs with a large glass plate. For 
 a vapor bath a double-walled vessel was employed and, some- 
 what as in Regnault's apparatus, the steam, after passing 
 through the inner vessel, reached the condenser by way of the 
 annular space beween the double walls. 
 
 In Regnault's constant-volume air thermometer the tension 
 of the gas was measured by a simple manometer open to the 
 
 K 153 
 
MEMOIRS ON 
 
 air ; consequently a baro- 
 metric reading had to be 
 made at the time the ver- 
 tical difference was deter- 
 mined between the two 
 mercury levels in the mano- 
 meter. The number of 
 readings involved in these 
 pressure measurements ad- 
 ded to the laboriousness of 
 the work and to the liabil- 
 ity to error in the results. 
 Regnault did not regard 
 his readings of heights of 
 mercury columns incorrect 
 by more than 0.01 centi- 
 meter, yet he considered 
 such an error always pos- 
 sible. To increase the accur- 
 acy of the tension measure- 
 ments was Chappuis's chief 
 
 Fia. 1. 
 
 154 
 
 Fio. 
 
EXPANSION OF GASES 
 
 care. For this purpose the apparatus was so arranged that but 
 one reading was necessary to give the total pressure exerted by 
 the gas in the reservoir. The platinum capillary tube (c in Fig. 1) 
 leads from the gas reservoir through the close-fitting steel plug 
 into the closed chamber shown in section and on a larger scale in 
 Fiy. 2. The mercury in this chamber is kept just in contact 
 with a fixed pointer, 0.5 millimeter long, projecting downward 
 from the plane under-surface of the steel plug, by raising or 
 lowering the mercury reservoir R connected with the mano- 
 metric chamber by a steel tube. This adjustment can be made 
 with the greatest exactness by means of a screw movement 
 attached to R. The difference between the mercury level in 
 the closed chamber and that in the open tubes M, M and R 
 which are all in communication with one another is a measure 
 of the excess of pressure in the gas reservoir over that of the 
 atmosphere. 
 
 Dipping in the open well Mis a barometer B attached to a 
 movable carriages which can be displaced along a vertical line 
 by means of the screw-rod s. The barometric chamber is pro- 
 vided with one or more black glass pointers fused to the side, 
 the tips of which turn downward along the line of the axis of 
 the chamber ; by means of s the barometer is raised or lowered 
 until the mercury meniscus just touches the tip of the pointer. 
 The apparatus is so constructed that the barometric chamber 
 and the manometric chamber are in the same vertical line ; hence 
 the total pressure upon the gas in the reservoir is measured by 
 the vertical distance between the menisci in B and n. The 
 tubing of which B, n, M and M' are made is of 2.5 centimeters 
 internal diameter, and hence the menisci show little curvature. 
 The position of the pointer in the manometric chamber with 
 respect to the scale attached to the support being once for all 
 known, a single reading, that of the pointer and meniscus in B, 
 suffices to show the total pressure on the gas in the reservoir. 
 
 The fact of the exact adjustment of all these levels was deter- 
 mined by means of cathetometer microscopes fitted with micro- 
 meter eyepieces. The heights were read off on a metal scale 
 attached to the manometer-support close to the manometer 
 tubes. 
 
 Eight mercury thermometers of hard glass were used : four 
 
 155 
 
MEMOIRS OK 
 
 were graduated from 5 to 104; the other four from 32 to 
 + 39 and from 95 to 103 , there being a reservoir on the stem 
 between 39 and 95. The thermometers of these two kinds 
 were about 70 centimeters and 54 centimeters long, respectively ; 
 the divisions corresponding to single degrees were over 5.5 mil- 
 limeters apart. Prior to the actual determinations most care- 
 ful calibration-tests were made upon the gas reservoir, the cap- 
 illary tube, the reading microscopes, the scale, the thermom- 
 eters, etc. The coefficient of expansion of the reservoir was 
 determined with another tube of the same alloy. 
 
 Nitrogen. The reservoir being filled with pure nitrogen, a 
 series of determinations were made of the pressure upon the gas 
 at 0. Of the 19 measurements, each the average of 3-7 read- 
 ings, the highest was 995.967 mm. ; lowest, 995.922 mm. ; mean, 
 995.942. These measurements were made on various days 
 extending through two months and a half. At intervals dur- 
 ing this period the pressure corresponding to a temperature of 
 100 was determined ; the figures, reduced to 45 latitude and 
 sea level, were : 
 
 No. Pressures Corresponding temperatures 
 
 1. 4 readings 1358.057mm. 100.0548 
 
 2. 6 1357.424 99.8826 
 
 3. 6 1356.479 99.6212 
 
 4. 6 1356.795 99.7160 
 
 From these pressures, assuming the mean value 995.942mm. 
 for the pressure at 0, the coefficients deduced are : 
 
 1. 0.00367482 
 
 2. 0.00367471 
 
 3. 0.00367468 
 
 4. 0.00367442 
 Mean, a = 0.00367466. 
 
 Elaborate comparisons were next made between four of the 
 mercury thermometers and the nitrogen thermometer at 15, 
 20, 25, 30, 35, 40, 45, 60.8 (boiling-point of chloro- 
 form) and 78 (that of alcohol). 
 
 A second series of determinations of the gas pressure at 
 (the room temperature being lower than in the former series), 
 gave, as a mean, 995.888 mm. Comparisons, on the assumption 
 that a =0.00367466, were made with the mercury thermometers 
 
 156 
 
EXPANSION OF OASES 
 
 of the second set at 2.5, 5, 10, 15, 20, 25, 4, 24, 
 20, 15, 10, 5 . The results of these comparisons are 
 shown in the form of a curve on page 158. 
 
 Carbon dioxide. Twelve measurements were made (each the 
 average of 4-8 readings) of the tension of the gas at 0, and 
 four of the tension at 100, as in the case of nitrogen. The 
 
 values deduced for a were : 
 
 0.00372458 
 0.00372483 
 0.00372481 
 0.00372486 
 
 Mean, a = 0.00372477. 
 
 Comparisons were again made with the mercury thermometers 
 a t_i7,-.lo , 10, 20, 30, 40, 
 
 Part of the gas having been allowed to escape from the 
 apparatus, so that the pressure at was reduced from about 1 
 meter of mercury to about 870 mm., nine measurements were 
 made at which ranged from 870.253 to 870.296 mm., and 
 five at about 100. The values of a obtained were : 
 
 0.00371629 
 0.00371631 
 0.00371646 
 0.00371629 
 0.00371635 
 
 Mean, a = 0.00371634. 
 
 Finally, the reservoir was filled with pure hydrogen obtained 
 by electrolysis. Two series of determinations of the tension at 
 were made, comprising a total of 23 measurements, each the 
 average of three readings, and seven determinations at 100. 
 The calculated values of a were : 
 
 0.00366271 
 0.00366248 
 0.00366225 
 0.00366231 
 0.00366256 
 0.00366270 
 0.00366269 
 
 Mean, a = 0.00366254. 
 
 Comparisons of the readings of the hydrogen- and mercury- 
 thermometers were made at 17 different temperatures between 
 24 and 78. 
 
 The curves showing the deviations of the nitrogen-, carbon- 
 dioxide- and hydrogen-thermometers from the mercury-ther- 
 
 157 
 
MEMOIRS ON 
 
 mometers are exhibited in Fig. 3. The maximum deviations 
 are : 
 
 For hydrogen, 0.107 at 40, 
 
 For nitrogen, 0.097 at 40 , 
 
 For carbon dioxide, 0.049 at 35. 
 
 It will be noted that from about 65 to 100 the value of a is 
 practically identical for hydrogen and nitrogen. 
 
 0.10- 
 
 05- 
 
 -20 -10 
 O.05 
 
 Of 10 - 
 
 FIG. 3 
 
 The coefficients of expansion for nitrogen and carbon dioxide 
 at temperatures ranging from 10 to 100 are thus stated by 
 Chappuis : 
 
 Nitrogen Carbon dioxide 
 
 0.00367781 0.00373807 
 
 7698 3538 
 
 7625 3273 
 
 7561 3019 
 
 7506 2779 
 
 7461 2558 
 
 7426 2360 
 
 2191 
 2054 
 1954 
 1896 
 1884 
 
 In the case of carbon dioxide, the change of the coefficient of 
 expansion with change of pressure, is given thus : 
 
 Initial Pressure Coefficient 
 
 999.18 0.00372477 
 
 870.28 0.00371634 
 
 158 
 
 Temperature 
 10 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 100 
 
EXPANSION OF GASES 
 
 Bibliography. 
 
 De Morveau and du Vernois: Annales de Chimie, [1] 1, 256-299 
 
 (1790). 
 
 Dalton: Memoirs of the Literary and Philosophical Society of 
 Manchester, 5 [Part 2], 595-602 (1802) ; Gilbert's Annalen, 12, 
 310-318 (1802). 
 
 Gay-Lussac : Annales de Chimie, [1] 43, 137-175 (1802) ; Gilbert's 
 Annalen, 12, 257-291 (1802). 
 
 Biot's Traite de Physique, 1, Chap. 9. 
 Gilbert: Gilbert's Annalen, 14, 267 (1803). 
 
 Dulong and Petit : Annales de Chimie et de Physique, [2] 2, 240- 
 254 (1816). 
 
 ditto. [2] 7, 113-136 (1817). 
 
 Flaugergues: Journal de Pharmacie, 77, 273; 83, 344; abstract, 
 
 Gehler's PhysiTcalisches Worterbuch, 1, 637-638 (1825). 
 Rudberg: Poggendorffs Annalen, 41, 271-293, 558-559 (1837). 
 
 ditto. 44, 119-123 (1838). 
 
 Magnus : Poggendorff's Annalen, 55, 1-27 (1842) ; abstract, Comptes 
 Rendus,14, 165; ditto. Annales de Chimie et de Physique, 
 [3] 4, 330-336 (1842). 
 
 Poggendorffs Annalen, 57,177-199 (1842); Annales de 
 Chimie et dePhysique, [3] 6, 353-369 (1842). 
 
 Regnault : Annales de Chimie et de Physique, [3] 4, 5-63 (1842) ; 
 Poggendorff 's Annalen,55, 391-414, 557-584 (1842) ; Memoires 
 de VAcademie des Sciences, 21, 15-120 (1847). 
 
 ditto, [3] 5, 52-83 (1842) ; ditto, 57,115-150 (1842) ; ditto, 21, 
 15-120 (1847). 
 
 ditto, [3] 5, 83-104 (1842) ; ditto, 57, 199-218 (1842). 
 ditto, [3] 6, 370-380 (1842). 
 ditto, [3] 26, 257-261 (1849). 
 
 Memoires de V Academie des Sciences, 21, 168-190 (1847). 
 
 ditto, 26, 565-580 (1862). 
 
 Recknagel: Poggendorff's Annalen, 123, 115-140 (1864). 
 Balf our Stewart: Philosophical Transactions, 153, 425-435 (1863). 
 v. Jolly: Poggendorff's Annalen, Jubelband, 82-97 (1874). 
 Mendeleeff and Kajander : abstract, Berichte der deutchen chemis- 
 chen Gesellschaft, 8, 1681 (1875). 
 
 ditto, 9, 1311 (1876) ; Comptes Rendus, 82, 450-454 (1876). 
 Mendeleeff: ditto, 1O, 81 (1877). 
 
 159 
 
MEMOIRS ON EXPANSION OF GASES 
 
 Amagat: Annalesde Chimie et de Physique, [4] 29, 246-285 (1873). 
 ditto. [5J 22, 353-398 (1881). 
 
 ditto. [6] 29, 68-136, 505-574 (1893). 
 
 Andrews: Philosophical Transactions, 166, 421-449 (1876). 
 Rowland : On the Mechanical Equivalent of Heat, Cambridge, 
 
 1880. 
 
 Crafts: Comptes Rendus, 95, 836-839 (1882). 
 
 Callendar: Philosophical Transactions, 178 A, 161-230 (1887); 
 abstract, Proceedings of the Royal Society, 41, 231-238 
 (1887). 
 
 Proceedings of the Royal Society, 5O, 247-251 (1891). 
 Callendar and Griffiths : Philosophical Transactions, 182 A, 119- 
 
 157 (1891). 
 
 Schiff : Zeitschrift der physikalische Chemie, 1, 68-69 (1887). 
 Chappuis : Travaux et Memoires du Bureau International des 
 Poids et Mesures, 6 (1888) ; Archives des Sciences (Geneve), 
 2O, 5-36, 153-179, 248-262 (1888). Rapports du Congres 
 International de Physique, Paris, 1900, 1. p. 131. 
 Grunmach and Pernet: Metronomische Beitrage, No. 3. 
 Wiebe and Bottcher : Zeitschrift fur Instrument enkunde, 10, 16- 
 
 28, 233-246 (1890). 
 
 Melander: Wiedermann's Annalen, 47, 136-154(1892). 
 Baly and Ramsay: Philosophical Magazine [5], 38, 301-327 (1894). 
 Kuenen and Randall: Proceedings of the Royal Society, 59, 60- 
 
 65 (1895). 
 Leduc: Journal de Physique, [3] 7, 201-209 (1898); Annales de 
 
 Chimie et de Physique, [71 15, 95-105 (1898). 
 Leduc and Sacerdote:AnnaZes de Chimie et de Physique,[7] 15, 
 
 60 (1898). 
 
 Harker and Chappuis: Philosophical Transactions, 194 A, 37-134 
 (1900). 
 
 160 
 
INDEX. 
 
 PAGE 
 
 A 
 Air, Coefficient of Expansion of : 
 
 Amagat, .,.. 11 
 
 Amontons, . . . . . . - .; 30 
 
 Bottcher and Wiebe, . . . . . 13 
 
 Callendar and Griffiths, . . . . .. 13 
 
 Dalton, . . . . . . go, 22 
 
 Flaugergues, . . . . . - v .,.- 5 
 
 Gay-Lussac, . ^ . , . . 43 
 
 Griffiths and Callendar, . . . ^ 13 
 
 v. Jolly, . . ; . . .. . 10 
 
 Magnus, . . . . . . 7 
 
 Melander, . . ,. . . 14 
 
 Mendeleefif, . . . . . . 11, 12 
 
 Priestley, . . . . . 34 
 
 Eegnault, . . V . 81, 89, 95, 100, 126, 134, 136, 143 
 
 Rudberg, . .. . . , , , . . . 6 
 
 Stewart, . . . . . .. . 9 
 
 Wiebe and Bottcher, . . . . .13 
 
 Air-scale and mercury-scale of temperature, 4, 104, 158 
 
 Amagat, . ... . 10 
 
 Ammonia, Coefficient of Expansion of : 
 
 Gay-Lussac, . . . . . 46 
 
 Priestley, . . . . . , 34 
 
 Regnault, . . . . . . 109 
 
 Amontons, . . . . . . . 30 
 
 Andrews, . . . . . . . 12 
 
 Argon, Coefficient of Expansion of: Kuenen and Randall, 14 
 
 B 
 
 Baly and Ramsay, . . . . .- . 15 
 
 Bettancourt, . . . . . . . 27 
 
 Berthollet, . ... ^ . . . 34 
 
 161 
 
INDEX. 
 
 Biot: Traite de Physique, . . . . 4, 51, 74, 106 
 
 Bohr, . . 15 
 
 Bottcher and Wiebe, 13 
 
 Boyle's Law, Variations from, . . 8, 10, 137, 144 
 
 C 
 
 Callendar and Griffiths, . . . . ; 13 
 
 Carbon dioxide, Coefficient of Expansion of: 
 
 Amagat, . . . . ... 10, 11 
 
 Andrews, . . . . v . . 12 
 
 Baly and Ramsay, . . . . .16 
 
 Chappuis, . . . . . . 13, 157 
 
 Dalton, . -.' . . ,;' . 21 
 
 Gay-Lussac, . . * . . 45 
 
 v. Jolly, ...-: . . ' . . . 10 
 
 Magnus, . . . -. . - . 7 
 
 Melander, . . . . . . 14 
 
 Mendeleeff , . . . . f . 12 
 
 Priestley, . . . v ^ . . . 34 
 
 Ramsay and Baly, . . . . . 16 
 
 Regnault, 109, 143 
 
 Carbon monoxide, Coefficient of Expansion of : 
 
 Regnault, ...... 109, 143 
 
 Chappuis, ... . / . . . 13, 151 
 
 Charles, ' ; . 37, 60 
 
 Constant Pressure, Coefficients at : Causes of differences, 147 
 
 Cyanogen, Coefficient of Expansion of : 
 
 Regnault, 109, 143, 147 
 
 Dalton, 3,17,22,59,71 
 
 Davy, 124 
 
 Deluc, 32 
 
 Dulong and Petit, . . . . . 4, 23, 103 
 
 Duvernois and de Morveau, ... 3, 20, 34 
 
 F 
 Flaugergues, ....... 5 
 
 G 
 
 Gay-Lussac, '. . . . .3,25,48,51,65,71,101 
 
 Gilbert, . \ . . 71 
 
 162 
 
INDEX. 
 
 Glass, Coefficient of Expansion of, . . 5, 21, 57, 79, 84, 103 
 
 Griffiths and Callendar, 13 
 
 Guyton de Morveau, . . . . . . 3, 20, 34 
 
 Harker and Chappuis, ..... 13 
 Helium, Coefficient of Expansion of: 
 
 Kuenen and Randall, . . . . 14 
 Hydrobromic Acid gas, Coefficient of Expansion of: 
 
 Mendeleeff, ..... 12 
 Hydrochloric Acid gas, Coefficient of Expansion of : 
 
 Gay-Lussac, . . . . . 45 
 
 Priestley, . . . . . 34 
 
 Regnault, 109 
 
 Hydrofluoric Acid gas, Coefficient of Expansion of : 
 
 Priestley, . . . ,.,. . . 34 
 Hydrogen, Coefficient of Expansion of : 
 
 Amagat, . . . . . 10,11 
 
 Baly and Ramsay, . . . . 15 
 
 Chappuis, . . . . . .13, 157 
 
 Dalton, . . . . . . 21 
 
 Gay-Lussac, . . . . 43 
 
 v. Jolly, . . . . . . 10 
 
 Magnus, . . % . . . 7 
 
 Melander, . . . . . 14 
 
 Mendeleeff, . / . ' .'.., . 12 
 
 Priestley, . . . . . . . 34 
 
 Ramsay and Baly, . . . . 15 
 
 Regnault, . . . . ' . . . 109, 143 
 
 Hydrogen-thermometer, Coefficient of: 
 
 Expansion used by Regnault v . > . 9 
 
 v. Jolly, . . . . .... 9, 12 
 
 Kajander and Mendeleeff, ... . . 11 
 
 Kelvin, Lord, . ... . . . . 9 
 
 Kuenen and Randall, . . ... . 14 
 
 163 
 
INDEX. 
 
 L 
 
 Lahire, . . . . . . . 31 
 
 Law of Expansion of Gases : 
 
 Amontons, . . . . . .30 
 
 Dalton, . . . . . . 21 
 
 Gay-Lussac, . . . . . , 48 
 
 Regnault, . . . . . -.150 
 
 M 
 
 Magnus, . . . . . * ^ 6,12,144 
 
 Manometer of Chappuis, ' . ; . : . . 155 
 
 " v. Jolly, . . ., . . ' . . 9 
 
 " Regnault, . . . . . . 90, 97, 127, 130 
 
 " Rudberg, '. , . ; . . 69 
 
 Mariotte's Law, Variations from Boyle and, _^ 10, 137, 144 
 
 Mayer, Tobias, . . . . . ' . . 60 
 
 Melander, . . . . . . . ; . 14 
 
 Mendeleeff, ~Y . . ... , . 11,16 
 
 Mercury, Coefficient of Expansion of, ... 4, 103 
 
 Mercury -scale, Comparison of, with gas-scales, . . 4, 158 
 
 Moisture, Effects of, . . .3, 19, 31, 37, 53 
 
 Monge, ........ 34 
 
 de Morveau (Guy ton), ...... 20 
 
 N 
 Nitrogen, Coefficient of Expansion of: 
 
 Amagat, ...... 11 
 
 Baly and Ramsay, ..... 15 
 
 Chappuis, . . . . . . 13, 156 
 
 and Barker, .... 13 
 
 Gay-Lussac, ...... 44 
 
 Harker and Chappuis, .... 13 
 
 v. Jolly, . . . . . 10 
 
 Priestley, .....*. 34 
 
 Ramsay and Baly, ..... 15 
 
 Nitrous oxide, Coefficient of Expansion of : 
 
 Dalton, . . ... . . 21 
 
 Gay-Lussac, . . ... . 46 
 
 Priestley, . . ... . 34 
 
 Regnault, . . . ... 109, 143 
 
 Nuguet, . . . . . . . . 31 
 
 164 
 
INDEX. 
 
 O 
 Oxygen, Coefficient of Expansion of: 
 
 Amagat, ....... 11 
 
 Baly and Ramsay, ..... 15 
 
 Bohr, ....... 16 
 
 Dalton, . . . . . . . 21 
 
 Gay-Lussac, ...... 43 
 
 v. Jolly, 10 
 
 Priestley, . . . . . 34 
 
 Eamsay and Baly, . . . . . 15 
 
 Regnault, 109 
 
 P 
 
 Pressure, Effect of decreased, on the Coefficient of Ex- 
 pansion of Gases : 
 
 Air, . . , . ,, ; .,' . 14, 126 
 
 Carbon dioxide, . .> . . . 14, 15 
 
 Hydrogen, . . . . . ^ . . 14, 15 
 
 Nitrogen, . . ' . .. . 15 
 
 Oxygen, , . . , . . 15 
 
 Pressure, Effect of increased, on the Capacity of glass 
 
 bulbs, .. . . . . . 132 
 
 Pressure, Effect of increased, on the Coefficient of Ex- 
 pansion of Gases : 
 
 Air, . . . . . 11, 12, 134, 143 
 
 Carbon dioxide, . . .11, 12, 136, 143, 157 
 Hydrogen, ..... 11, 12, 143 
 
 Nitrogen, ...... 11 
 
 Oxygen, ...... 11 
 
 Preston's Theory of Heat, ..... 73 
 
 Priestley, ........ 33 
 
 R 
 
 Ramsay and Baly, . ~ . . . . . 15 
 
 Randall and Kuenen, ...... 14 
 
 Recknagel, . . . . . . . 9 
 
 Regnault, 3, 7, 12, 63, 120, 121, 153 
 
 RoiorRoy, 19,33 
 
 Roscoe, . . . . . . . 3 
 
 Rudberg, . ' . . . . . . 4, 5, 65 
 
 165 
 
INDEX. 
 
 S 
 de Saussure, . . . . . . .33 
 
 Siljestrom, ....... 16 
 
 Stancari, . 32 
 
 Stewart, ........ 9 
 
 Sulphur dioxide, Coefficient of Expansion of : 
 
 Amagat, ...... 10 
 
 Gay-Lussac, . . . . . . . 46 
 
 Magnus, ..... .. 7 
 
 Priestley, 34 
 
 Regnault, . . . . . 109,143,146 
 
 Temperatures, Coefficients of Expansion of Gases at high, 10 
 
 " " " "very low, 9 
 
 " on gas and mercury-scales, . '? 4, 104, 158 
 
 V 
 
 Vandermonde, . ; * . . . . ? 34 
 
 Vapors, Expansion of, . . . . . . 47, 150 
 
 W 
 
 Water- vapor, Effect of, in gases, . . .3, 19, 31, 37, 53 
 
 Wiebe and Bottcher, . . . . . , . 13 
 
 Ziegler, . ,. 27 
 
 166 
 
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