REESE LIBRARY 
 
 OF THK 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Deceived , igo . 
 
 Accession No. 83054 Class No. 
 
HARPER'S SCIENTIFIC MEMOIRS 
 
 EDITED BY 
 
 J. S. AMES, PH.D. 
 
 PKOKKSSOK OK PHYSICS IN JOHNS HOPKINS UNIVERSITY 
 
 V. 
 THE LAWS OF GASES 
 
THE LAWS OF GASES 
 
 MEMOIRS BY ROBERT BOYLE AND 
 E. H. AMAGAT 
 
 TRANSLATED AND EDITED BY 
 
 CARL BARUS 
 
 PROFESSOR OF PHYSICS IN BROWN UNIVERSITY 
 I 
 
 NEW YORK AND LONDON 
 
 HARPER & BROTHERS PUBLISHERS 
 1899 
 
HARPER'S SCIENTIFIC MEMOIRS, 
 
 EDITED BY 
 
 J. S. AMKS, PH.D., 
 
 PKOFKSSOR OF PHYSICS IN JOHNS HOPKINS UNIVKK8ITY. 
 
 SOW READY: 
 
 THE FREE EXPANSION OF GASES. Memoirs 
 by Gay-Lussac, Joule, and Jonle and Thomson. 
 Editor, Prof. J. S. AMKS, Ph.D., .Johns Hopkins 
 University. 75 cents. 
 
 PRISMATIC AND DIFFRACTION SPECTRA. 
 Memoirs by Joseph von Fraunhofer. Editor, Prof. 
 J. S. AMKS, Ph.D., Johns Hopkins University. 
 GO cents. 
 
 RONTGEN RAYS. Memoirs by Rontgen, Stokes, 
 and J. J. Thomson. Editor, Prof. GKOKGK F. 
 BAEKKR, University of Pennsylvania. GO cents. 
 
 THE MODERN THEORY OF SOLUTION. Me- 
 moirs by Pfeffer, Van't^Hoff, Arrhenius, and Raoult. 
 Editor, Dr. H. C. JONKS, Johns Hopkins University. 
 $100. 
 
 THE LAWS OF GASES. Memoirs by Boyle and 
 Amagat. Editor, Prof. C A ur, BAUDS, Brown University. 
 
 fX PREPARATION: 
 
 THE SECOND LAW OF THERMODYNAMICS. 
 Memoirs by Caruot, Clausius, and Thomson. Editor, 
 Prof. W. F. MAGIK, Princeton University. 
 
 THE FUNDAMENTAL LAWS OF ELECTRO- 
 LYTIC CONDUCTION. Memoirs by Faraday, 
 Hittorf, and Kohlransch. Editor, Dr. H. M. GOOD- 
 WIN, Massachusetts Institute of Technology. 
 
 THE EFFECTS OF A MAGNETIC FIELD ON 
 RADIATION. Memoirs by Faraday, Kerr, and 
 Zeeinan. Editor, Dr. E. P. LKWIS, University of 
 California. 
 
 WAVE-THEORY OF LIGHT. Memoirs by Hnygens, 
 Young, and Fresnel. Editor, Prof. HKNKY CHEW, 
 Northwestern University. 
 
 NEWTON'S LAW OF GRAVITATION. Editor, 
 Prof. A. S. MACKKNZIK, Bryn Mawr College. 
 
 NEW YORK AND LONDON: 
 
 HARPER & BROTHERS, PUBLISHERS. 
 
 Copyright, 1899, by HAKPEK & BKOTUKKS. 
 
 All rights reserved. 
 
PKEFACE 
 
 OF course anybody may read the famous Memoirs of Ama- 
 gat in the original; but everybody cannot so easily get these 
 papers permanently into his possession. I believe, therefore, 
 with the present translations to have scored a point in the in- 
 terest of accessibility, and thus to have materially contributed 
 to the advancement of science. 
 
 C. B. 
 
 BROWN UNIVERSITY, Providence, R. I., 
 March, 1899. 
 
 83054 
 
GENERAL CONTENTS 
 
 HAGK 
 
 Preface v 
 
 A Defence of the Doctrine Touching the Spring and Weight of the 
 
 Air, proposed by Mr. R. BOYLE in his new Physico-Mechan- 
 
 ical Experiments, against the Objections of Franciscus Linus. 3 
 
 Biographical Sketch of Boyle 10 
 
 On the Compressibility of Gases at High Pressures. By E. H. Amagat 13 
 On the Elasticity and the Thermal Expansion of Fluids Throughout 
 
 an Interval Terminating in Very High Pressures. By E. H. 
 
 Amagat 53 
 
 Biographical Sketch of Amagat 107 
 
 Bibliography 108 
 

 A DEFENCE OF 
 
 THE DOCTEINE TOUCHING THE SPEING 
 AND WEIGHT OF THE AIE 
 
 Proposed by Mr. R. BOYLE in his New Physico- Mechanical Experiments,. 
 
 against the Objections of FHANCISCUS LINUS, wherewith the 
 
 Objector's Funicular Hypothesis is also Examined 
 
 London, 1662 
 
A DEFENCE OF 
 
 THE DOCTRINE TOUCHING THE SPRING 
 AND WEIGHT OF THE AIR* 
 
 BY ROBERT BOYLE 
 
 PART II., CHAPTER V. 
 
 TWO NEW EXPERIMENTS TOUCHING THE MEASURE OP THE FORCE OP THE 
 SPRING OF AIR COMPRESSED AND DILATED 
 
 We took then a long glass-tube, which, by a dexterous hand 
 and the help of a lamp, was in such a manner crooked at the 
 bottom, that the part turned up was almost parallel to .the rest 
 of the tube, and the orifice of this shorter leg of the siphon (if 
 I may so call the whole instrument) being hermetically sealed, 
 the length of it was divided into inches (each of which was 
 subdivided into eight parts) by a streight list of paper, which 
 containing those divisions, was carefully pasted all along it. 
 Then putting in as much quicksilver as served to fill the arch 
 or bended part of the siphon, that the mercury standing in a 
 level might reach in the one leg to the bottom of the divided 
 paper, and just to the same height or horizontal line in the 
 other ; we took care, by frequently inclining the tube, so that 
 the air might freely pass from one leg into the other by the 
 sides of the mercury (we took, I say, care) that the air at last 
 included in the shorter cylinder should be of the same laxity 
 with the rest of the air about it. This done, we began to pour 
 quicksilver into the longer leg of the siphon, which by its weight 
 pressing up that in the shorter leg, did by degrees streighten 
 
 * Selected from Boyle's New Physico - Mechanical Experiments, Lon- 
 don, 1662. 
 
 3 
 
MEMOIRS, ON 
 
 the included air : and continuing this pouring in of quicksilver 
 till the air in the shorter leg was by condensation reduced to 
 take up but half the space it possessed (I say, possessed, not 
 filled) before ; we cast our eyes upon the longer leg of the glass, 
 on which was likewise pasted a list of paper carefully divided 
 into inches and parts, and we observed, not without delight 
 and satisfaction, that the quicksilver in that longer part of the 
 tube was 29 inches higher than the other. Now that this 
 observation does both very well agree with and confirm our 
 hypothesis, will be easily discerned by him that takes notice 
 what we teach ; and Monsieur Paschal and our English friend's 
 experiments prove, that the greater the weight is that leans 
 upon the air, the more forcible is its endeavour of dilatation, 
 and consequently its power of resistance (as other springs are 
 stronger when bent by greater weights). For this being con- 
 sidered, it will appear to agree rarely-well with the hypothesis, 
 that as according to it the air in that degree of density and 
 correspondent measure of resistance, to which the weight of 
 the incumbent atmosphere had brought it, was able to counter- 
 balance and resist the pressure of a mercurial cylinder of about 
 29 inches, as we are taught by the Torricellian experiment ; 
 so here the same air being brought to a degree of density about 
 twice as great as that it had before, obtains a spring twice as 
 strong as formerly. As may appear by its being able to sustain 
 or resist a cylinder of 29 inches in the longer tube, together 
 with the weight of the atmospherical cylinder, that leaned upon 
 those 29 inches of mercury; and, as we just now inferred from 
 the Torricellian experiment, was equivalent to them. 
 
 We were hindered from prosecuting the trial at that time 
 by the casual breaking of the tube. But because an accurate 
 experiment of this nature would be of great importance to the 
 doctrine of the spring of the air, and has not yet been made 
 (that I know) by any man ; and because also it is more uneasy 
 to be made than one would think, in regard of the difficulty as 
 well of procuring crooked tubes fit for the purpose, as of making 
 a just estimate of the true place of the protuberant mercury's 
 surface ; I suppose it will not be unwelcome to the reader to be 
 informed, that after some other trials, one of which we made 
 in a tube whose longer leg was perpendicular, and the other, 
 that contained the air, parallel to the horizon, we at last pro- 
 cured a tube of the figure expressed in the scheme; which 
 
 4 
 
OF THE 
 
 UNIVERSl' 
 
 THE LA 
 
 OF .GASES 
 
 tube, though of a pretty bigness, was so long, that the cylinder, 
 whereof the shorter leg of it consisted, admitted a list of paper, 
 which had before been divided into 12 inches and their quarters, 
 and the longer leg admitted another list of paper of divers feet 
 in length, and divided after the same manner. Then quicksilver 
 being poured in to fill up the bended part of the glass, that the 
 surface of it in either leg might rest in the same horizontal line, 
 as we lately taught, there was more and more quicksilver poured 
 into the longer tube ; and notice being watchfully taken how 
 far the mercury was risen in that longer tube, when it appeared 
 to have ascended to any of the divisions in the shorter tube, 
 the several observations that were thus successively made, and 
 as they were made set down, afforded us the ensuing table : 
 
 A TABLE OF THE CONDENSATION" OP THE AIR 
 
 A 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 
 48 
 
 12 
 
 00 
 
 
 29* 
 
 29* 
 
 A A. The number of equal 
 
 46 
 44 
 
 11* 
 
 11. 
 
 01* 
 
 02f| 
 
 
 30^ 
 
 33^ 
 
 spaces in the shorter 
 leg, that contained the 
 same parcel of air di- 
 
 42 
 
 m 
 
 04y^- 
 
 
 33* 
 
 33J 
 
 versely extended. 
 
 40 
 
 10 
 
 06A 
 
 
 35* 
 
 35 
 
 
 38 
 
 91. 
 
 07H 
 
 
 37 
 
 36^f 
 
 B. The height of the mer- 
 
 36 
 34 
 32 
 
 9 
 
 8* 
 
 8 
 
 ipA 
 
 ISA 
 
 02 
 <D 
 
 39 I! 
 
 38| 
 41* 
 43# 
 
 curial cylinder in the 
 longer leg, that com- 
 pressed the air into 
 those dimensions. 
 
 30 
 
 7 
 
 17 
 
 a 
 
 47 T V 
 
 46| 
 
 
 28 
 
 7 
 
 21 3 
 
 s 
 
 50* 
 
 50 
 
 C. The height of the mer- 
 
 26 
 24 
 23 
 
 6* 
 
 6 . 
 
 25A 
 
 89ft 
 
 3*A 
 
 o 
 
 54* 
 
 58H 
 
 58f 
 60H 
 
 curial cylinder, that 
 counterbalanced the 
 pressure of the atmos- 
 phere. 
 
 22 
 
 5j 
 
 34^-f- 
 
 0) 
 
 64* 
 
 63 1 T 
 
 
 21 
 
 
 37^f 
 
 r d 
 n 
 
 67* 
 
 
 D. The aggregate of the 
 
 20 
 
 5 
 
 41* 
 
 
 
 70 
 
 two last columns, j?and 
 
 19 
 
 
 1 6 
 
 45 
 
 
 74 * 
 
 
 (7, exhibiting the press- 
 ure sustained by the 
 
 18 
 
 4 
 
 48yf 
 
 
 77-J-f 
 
 77f 9 
 
 included air. 
 
 17 
 
 4J 
 
 53H 
 
 
 82i| 
 
 82 T \ 
 
 
 16 
 
 4 
 
 58-fr 
 
 
 87f| 
 
 87| 
 
 E. What that pressure 
 
 15 
 14 
 
 3 f 
 
 63H 
 
 
 93 T V 
 100 T V 
 
 93* 
 
 99f 
 
 should be according to 
 the hypothesis, that 
 supposes the pressures 
 
 13 
 
 3 
 
 78^|- 
 
 
 107 ff 
 
 17* 
 
 and expansions to be in 
 
 12 
 
 3 
 
 88* 
 
 
 117* 
 
 116f 
 
 reciprocal proportion. 
 
 5 
 
MEMOIRS ON 
 
 For the better understanding of this experiment, it may not 
 be amiss to take notice of the following particulars : 
 
 1. That the tube being so tall that we could not conveniently 
 make use of it in a chamber, we were fain to use it on a pair 
 of stairs, which were yet very lightsome, the tube being for 
 preservation's sake by strings so suspended that it did scarce 
 touch the box presently to be mentioned. 
 
 2. The lower and crooked part of the pipe was placed in a 
 square wooden box, of a good largeness and depth, to prevent 
 the loss of the quicksilver, that might fall aside in the transfu-' 
 sion from the vessel into the pipe, and to receive the whole 
 quicksilver in case the tube should break. 
 
 3. That we were two to make the observation together, the 
 one to take notice at the bottom, how the quicksilver rose in 
 the shorter cylinder, and the other to pour in at the top of the 
 longer ; it being very hard and troublesome for one man alone 
 to do both accurately. 
 
 4. That the quicksilver was poured in but by little and 
 little, according to the direction of him that observed below : 
 it being far easier to pour in more than to take out any, in case 
 too much at once had been poured in. 
 
 5. That at the beginning of the operation, that we might the 
 more truly discern where the quicksilver rested from time to 
 time, we made use of a small looking-glass held in a conven- 
 ient posture to reflect to the eye what we desired to discern. 
 
 6. That when the air was so comprest as to be crouded 
 into less than a quarter of the space it possessed before, we 
 tried whether the cold of a linen cloth dipped in water would 
 then condense it. And it sometimes seemed a little to shrink, 
 but not so manifestly that we dare build anything upon it. 
 We then tried likewise, whether heat would, notwithstanding 
 so forcible a compressure, dilate it ; and approaching the flame 
 of a candle to that part where the air was pent up, the heat 
 had a more sensible operation than the cold had before ; so 
 that we scarce doubted, but that the expansion of the air would, 
 notwithstanding the weight that comprest it, have been made 
 conspicuous, if the fear of unseasonably breaking the glass had 
 not kept us from increasing the heat. 
 
 Now although we deny not, but that in our table some par- 
 ticulars do not so exactly answer to what our formerly men- 
 tioned hypothesis might perchance invite the reader to expect ; 
 
 6 
 
THE LAWS OF GASES 
 
 yet the variations are not so considerable, but that they may 
 probably enough be ascribed to some such want of exactness 
 us in such nice experiments is scarce avoidable. But for all 
 that, till further trial hath more clearly informed me, I shall 
 not venture to determine whether or no the intimated theory 
 will hold universally and precisely, either in condensation of 
 air or rarefaction : all that I shall now urge being, that however 
 the trial already made sufficiently proves the main thing, for 
 which I here allege it ; since by it, it is evident, that as com-\ ' 
 mon air, when reduced to half its wonted extent, obtained near 
 about twice as forcible a spring as it had before ; so this thus) 
 comprest air being further thrust into half this narrow room, 
 obtained thereby a spring about as strong again as that it last 
 had, and consequently four times as strong as that of the com- 
 mon air. And there is no cause to doubt, that if we had been 
 here furnished with a greater quantity of quicksilver and a 
 very strong tube, we might, by a further compression of the 
 included air, have made it counterbalance the pressure of a far 
 taller and heavier cylinder of mercury. For no man perhaps 
 yet knows how near to an infinite compression the air may be 
 capable of, if the compressing force be competently increased. 
 
 And to let you see, that we did not (as a little above) incon- 
 siderately mention the weight of the incumbent atmospherical 
 cylinder as a part of the weight resisted by the imprisoned air, 
 we will here annex, that we took care; when the mercurial cyl- 
 inder in the longer leg of the pipe was about an hundred inches 
 high, to cause one to suck at the open orifice ; whereupon (as 
 we expected) the mercury in the tube did notably ascend. . . . 
 And therefore we shall render this reason of it that the press- 
 ure of the incumbent air being in part taken off by its ex- 
 panding itself into the sucker's dilated chest, the imprisoned 
 air was thereby enabled to dilate itself manifestly, and repel 
 the mercury, that comprest it, till there "was an equality of 
 force betwixt the strong spring of that comprest air on the 
 one part, and the tall mercurial cylinder, together with the 
 contiguous dilated air, on the other part. 
 
 Now, if to what we have thus delivered concerning the com- 
 pression of the air, we add some observations concerning its 
 spontaneous expansion, it will the better appear, how much 
 the phenomena of these mercurial experiments depend upon 
 
 7 
 
MEMOIRS ON 
 
 the differing measures of strength to be met with in the air's 
 spring, according to its various degrees of compression and 
 laxity. 
 
 A TABLE OF THE RAREFACTION OF THE AIR 
 
 
 A 
 
 B 
 
 
 
 D 
 
 E 
 
 A. The number of equal spaces at 
 
 1 
 
 00{f 
 
 
 29| 
 
 29} 
 
 the top of the tube, that con- 
 tained the same parcel of air. 
 
 2 
 
 io| 
 
 lof 
 
 
 19| 
 
 19f 
 
 
 3 
 
 204 
 
 
 9| 
 
 9.^5. 
 
 B. The height of the mercurial cyl- 
 
 4 
 
 224 
 
 CO 
 
 
 
 H 
 
 w 
 
 inder, that together with the 
 
 5 
 
 24-J 
 
 1 
 
 5 ! 
 
 5^f 
 
 spring of the included air coun- 
 
 6 
 
 24} 
 
 
 
 4f^ 
 
 terbalanced the pressure of the 
 
 7 
 
 
 OS 
 
 41 
 
 4 1 
 
 atmosphere. 
 
 8 
 
 26 
 
 B 
 
 si 
 
 344 
 
 
 9 
 
 264 
 
 2 
 
 3| 
 
 3^| 
 
 C. The pressure of the atmosphere. 
 
 10 
 
 264 
 
 tj 
 
 3* 
 
 w 
 
 
 12 
 
 27-J- 
 
 .j-j 
 
 2| 
 
 2 
 
 
 14 
 
 274 
 
 g 
 
 2-| 
 
 2-| 
 
 D. The complement of B to C, ex- 
 
 16 
 
 274 
 
 - 
 
 2-J 
 
 l|f 
 
 hibiting the pressure sustained 
 by the included air. 
 
 18 
 20 
 
 n 
 
 p 
 dp 
 
 4 
 
 
 
 24 
 
 284 
 
 
 it 
 
 ill 
 
 K. What that pressure should be, 
 
 28 
 
 284 
 
 
 H 
 
 1 T V 
 
 according to the hypothesis. 
 
 32 
 
 284 
 
 
 if 
 
 Olil 
 
 To make the experiment of the debilitated force of expanded 
 air the plainer, it will not be amiss to note some particulars, 
 especially touching the manner of making the trial ; which 
 (for the reasons lately mentioned) we have made on a light- 
 some pair of stairs, and with a box also lined with paper to 
 receive the mercury that might be spilt. And in regard it 
 would require a vast and in few places procurable quantity 
 of quicksilver, to imploy vessels of such kind as are ordinary 
 in the Torricellian experiment, we made use of a glass-tube of 
 about six feet long ; for that being hermetically sealed at one 
 end, served our turn as well as if we could have made the ex- 
 periment in a tub or pond of seventy inches deep. 
 
 Secondly, We also provided a slender glass-pipe of about the 
 
 8 
 
THE LAWS OF GASES 
 
 bigness of a swan's quill, and open at both ends ; all along 
 which was pasted a narrow list of paper, divided into inches 
 and half quarters. 
 
 Thirdly, This slender pipe being thrust down into the greater 
 tube almost filled with quicksilver, the glass helped to make it 
 swell to the top of the tube ; and the quicksilver getting in at 
 the lower orifice of the pipe, filled it up until the mercury in- 
 cluded in that was near about a level with the surface of the 
 surrounding mercury in the tube. 
 
 Fourthly, There being, as near as we could guess, little more 
 than an inch of the slender pipe left above the surface of the 
 restagnant mercury, and consequently unfilled therewith, the 
 prominent orifice was carefully closed with sealing wax melted; 
 after which the pipe was let alone for a while, that the air, 
 dilated a little by the heat of the wax, might, upon refrigera- 
 tion, be reduced to its wonted density. And then we observed 
 by the help of the above mentioned list of paper, whether we 
 had not included somewhat more or somewhat less than an 
 inch of air ; and in either case we were fain to rectify the error 
 by a small hole made (with a heated pin) in the wax, and after- 
 wards closed up again. 
 
 Fifthly, Having thus included a just inch of air, we lifted up 
 the slender pipe by degrees, till the air was dilated to an inch, 
 an inch and an half, two inches, &c., and observed in inches 
 and eighths the length of the mercurial cylinder, which at each 
 degree of the air's expansion was impelled above the surface of 
 the restagnant mercury in the tube. 
 
 Sixthly, The observations being ended, we presently made 
 the Torricellian experiment with the above-mentioned great 
 tube of six feet long, that we might know the height of the 
 mercurial cylinder, for that particular day and hour ; which 
 height we found, to be 29| inches. 
 
 Seventhly, Our observations made after this manner fur- 
 nished us with the preceding table, in which there would not 
 probably have been found the difference here set down betwixt 
 tho force of the air, when expanded to double its former dimen- 
 sions, and what that force should have been precisely according 
 to the theory, but that the included inch of air received some 
 little accession during the trial ; which this newly mentioned 
 difference making us suspect, we found byreplunging the pipe 
 into the quicksilver, that the included air had gained about 
 
 9 
 
 OF THK 
 
 UNIVERSITY 
 
MEMOIRS ON THE LAWS OF GASES 
 
 half an eighth, which we guessed to have come from some little 
 aerial bubbles in the quicksilver, contained in the pipe (so easy 
 is it in such nice experiments to miss of exactness). 
 
 The Honorable ROBERT BOYLE was born in Ireland, County 
 Cork, January 25, 1626, and died in London, December 30, 
 1691. He made his home in Oxford from 1654 to 1668, when 
 he moved to London. It was while living at Oxford that he 
 invented the air-pump, which was perfected for him in 1658 
 or 1659 by his assistant in chemistry, Robert Hooke, who was 
 afterwards so famous. In 1663, at the incorporation of the 
 Royal Society by King Charles II., Boyle wao appointed by the 
 charter one of the council, as he had been one of the persons 
 to whom the society owed its origin. He was elected president 
 of the society in November, 1680; but on account of "the 
 obligation to take the test and oaths," he felt obliged to de- 
 cline the honor. 
 
 It was in 1660 that he published his first experiments, On 
 the Spiring of the Air, and in 1662 that he announced the law 
 of gases that bears his name. These experiments were repeat- 
 ed later, by Mariotte in France, and were published by him in 
 1676. 
 
 Boyle published a great many papers in the Philosophical 
 Transactions, and was actively engaged in scientific work up to 
 the last years of his life. It is worthy of note that nearly all 
 the common lecture -experiments in hydrostatics and pneu- 
 matics are due to Boyle. 
 
ON THE OOMPEESSIBILITY OF GASES AT 
 HIGH PRESSURES 
 
 BY 
 
 E. H. AMAGAT 
 
 (Annales de Chimie et de Physique, 5 e serie, t. xxil, pp. 353-398, 1881) 
 
CONTENTS 
 
 PAGE 
 
 Introductory 13 
 
 Description of the Apparatus 15 
 
 Method of Experimentation 19 
 
 Method of Calculation , 20 
 
 Numerical Results 23 
 
 Examination and Discussion of the Results 26 
 
 Dilatation of Gases at High Pressures 36 
 
 Covolume Atomic Volume , . 39 
 
ON THE COMPRESSIBILITY OF GASES AT 
 HIGH PRESSURES 
 
 BY E. H. AMAGAT 
 
 INTRODUCTORY 
 
 IN 1869, when I communicated the results of my first experi- 
 ments relative to the effect of temperature on the compressi- 
 bility of a gas, no direct experiments had been made on this 
 subject. It was customary merely to quote Regnault's infer- 
 ences touching the behavior of carbon dioxide at 100 C. At 
 this temperature, since the density of the gas is sensibly in- 
 dependent of pressure for pressures in the neighborhood of 1 
 atmosphere, one may conclude that under the conditions stated 
 the gas appreciably follows Mariotte's law. Nevertheless, the 
 inference of Regnault is in need of slight modification. My 
 results proved that at 100, carbon dioxide, although diverging 
 less from the law than at ordinary temperatures, is quite sen- 
 sibly divergent; and M. Blaserna showid^ a short time after- 
 wards that the discrepancy arose out of an error which slipped 
 into the numerical calculations of Eegnault. Indeed, M. Bla- 
 serna arrived at an analogous conclusion himself in a purely theo- 
 retical paper published in the Annales de Chimie et de Physique 
 in 1865 (t. v.). 
 
 In 1872 I made a complete publication f of my researches on 
 this subject, having studied ammonia as far as 100, sulphur 
 dioxide and carbon dioxide as far as 250, and air and hydrogen 
 up to 320. 
 
 I then believed that at temperatures sufficiently low all gases 
 
 * Oomptes Eendus des /Seances de I'Academie des Sciences, t. xlix., 1869. 
 t Annales de Chimie et de Physique, t. xxix., 1873. 
 
 13 
 
MEMOIRS ON 
 
 behave like carbon dioxide ; but that as temperature increases 
 gases begin more and more to follow the law of Mariotte, finally 
 to depart from it indefinitely in a contrary sense as does hy- 
 drogen at ordinary atmospheric temperatures. It follows nat- 
 urally that nitrogen, which, as I showed, obeys Mariotte's law 
 as far as 100 and between 1 and 2 atmospheres, presents a neg- 
 ative discrepancy below that temperature ; and that hydrogen 
 more and more highly heated continues to present an in- 
 variably negative divergence of increasing value. Experiment, 
 however, has shown me that at 200 the divergence of air al- 
 ways sensibly zero does not from the shape of the curves tend 
 to become negative, and that even for the case of hydrogen 
 the discrepancy tends rather to vanish than to increase in the 
 negative direction or to remain negative. Naturally I then in- 
 ferred that the effect of temperature was an approach of both 
 gases towards the law, the compressibility of the first being di- 
 minished and that of the other increased. 
 
 It will be seen in the course of the present paper that this 
 conclusion is correct relative to hydrogen, but that for air the 
 interpretation of the results will have to be changed. It will 
 also be seen that it must be impossible to arrive at a knowledge 
 of the general laws for gases as long as the investigations are 
 limited to an interval of pressure within which the trend of 
 the discrepancies hardly even begins to appear ; that these laws 
 will not be manifest in their entirety until the experiments are 
 pushed forward throughout several hundred atmospheres; that, 
 finally, all that has hitherto been known about the compressi- 
 bility of gases would not have enabled any one to even suspect 
 the laws in their true characters, such as I shall establish them 
 below. 
 
 I shall not enter into any details as to the formulas by aid 
 of which different physicists have sought to express the effect 
 of temperature on the compressibility of gases. These for- 
 mulas, as a rule purely empyric, are not applicable except within 
 very narrow pressure-limits; moreover, I shall have occasion to 
 speak of them in the near future in a paper referring specially 
 to low pressures. 
 
 During the course of my experiments I was able to show that, 
 even after making allowance for atomic volume, the shortcom- 
 ings of Mariotte'*s law cannot be explained fully by postulat- 
 ing an internal pressure tending to move the molecules nearer 
 
 14 
 
THE LAWS OF GASES 
 
 together, because this pressure would be different for the same 
 mean distance of the molecules at different temperatures. I 
 shall return to this point below, and then complete the demon- 
 stration by comparing the results at which I have arrived with 
 those predicted by the theory of M. Him. 
 
 Eecently M. Winkelmann has published the results of experi- 
 ments made with ethylene between and 100 and between 
 1 and 2 atmospheres. He finds, corroboratively, that at 100 
 ethylene obeys the law of Mariotte more nearly than at C. 
 This is precisely my deduction for all the gases treated up to 
 100, 250, and 320. 
 
 With the exception of these experiments and those described 
 in the classical memoir of Andrews on the critical point, I 
 believe that no other experimental data are available, barring 
 the results which I adduced in the memoir summarizing my 
 experiments. 
 
 As to laws treating of the manner in which the compressi- 
 bility of a gas is modified at high pressures throughout different 
 temperatures, they are quite unknown. It was, therefore, with 
 the purpose of filling this important gap that I undertook the 
 researches which make up the subject of the present memoir. 
 
 I have studied the gases nitrogen, hydrogen, marsh gas, 
 ethylene, and carbon dioxide. As for air, and particularly 
 oxygen, I fear that at the higher temperatures the action of 
 the latter gas on mercury will be too rapid to admit of the 
 necessary measurements, and this in greater degree as the 
 experiments are more prolonged under the conditions of high 
 temperatures stated. 
 
 At ordinary temperatures, on the other hand, the experi- 
 ments can be conducted with relatively great despatch. A 
 series of six determinations may be made with rigor in a 
 quarter of an hour, and then all oxidation is inappreciable. 
 Hence, in my first research I was able to study these two gases 
 (by the method of comparison) without being annoyed by the 
 difficulty in question. It is my object, moreover, to make a 
 special study of it at some other time. 
 
 DESCRIPTION OF THE APPARATUS 
 
 The apparatus of which I here make use is the same which 
 has already served me in the determination at ordinary 
 
 15 
 
MEMOIRS ON 
 
 temperatures of the compressibility of the gases air, oxygen, 
 hydrogen, carbon dioxide, marsh gas, and ethylene, in com- 
 parison with nitrogen. I have briefly referred to it in my 
 first memoir without giving a full description. However, as 
 on that occasion I entered with considerable detail into the 
 construction of divers parts of this class of instruments, I am 
 able to confine myself to narrower limits here. 
 
 Figure 1 shows the apparatus drawn to a scale of one-twelfth 
 actual size. On the right hand is the nitrogen manometer.* 
 It has the identical dimensions and is mounted in quite the 
 same manner as the one on the machine described in my first 
 memoir on the subject. In this case it was used to measure 
 the compressibility of nitrogen in the Verpilleux mine shaft. 
 The jacket through which the current of water circulates and 
 the enclosed thermometer are attached in the same way. The 
 lid or flange which carries the whole is secured by four bolts to 
 a hollow block of cast-iron, in the cavity of which the reservoir 
 of the manometer is situated. On one side is a small wheel by 
 which a cylindrical plunger, passing through a long box stuffed 
 with leather, may be actuated for the purpose of regulating the 
 applied pressure or of bringing the mercury meniscus in the 
 stem of the manometer upon any division mark determined in 
 advance. This pressure was calculated from the known com- 
 pressibility of nitrogen. 
 
 On the left hand of the figure is another massive hollow 
 block carrying a manometer, within which is the gas to be com- 
 pared with nitrogen. This part is more bulky than the former, 
 and as a whole similar to the apparatus described in my first 
 memoir. Indeed, the experiments then treated might in any 
 case be repeated with it. The difference lies merely in details 
 of construction, and principally in the disposition of the stop- 
 cocks. Only the right half of this large block is to be used in 
 the experiments with which we are here concerned. The left 
 half of this part of the figure, carrying a lid with three bolts, 
 may be overlooked. In the earlier manometric experiments 
 the lower end of the hollow steel filament which ran to the top 
 of the mine shaft was here affixed. [See couplings attached.] 
 
 *In the Comptes Eendus, April 12, 1880, I showed that under the influ- 
 ence of pressure applied in the interior only these manometers are not 
 subject to an increase of volume serious enough to make special corrections 
 necessary. 
 
 16 
 
THE LAWS OF GASES 
 
 FIG. 1. APPARATUS FOR THE COMPRESSION OF GASES AT DIFFERENT TKMPKRATCRES 
 
 B 
 
MEMOIRS ON 
 
 If the observations are to be made at atmospheric tempera- 
 tures, the manometer containing the second gas is jacketed in 
 exactly the same way as the nitrogen manometer. If, however, 
 the observations are to be made at higher temperatures, the 
 glass tube with circulating water is replaced by a rectangular 
 trough, or vapor bath, supported on three iron columns, screwed 
 to the lid of the same block of iron which holds the manometer. 
 For this reason the lid is circular and a little too large, jutting 
 out slightly beyond the block to which it is bolted. 
 
 The trough was cast of a single piece of brass. On opposed 
 faces it is provided with two long and narrow windows, closed 
 with plate-glass held in place by brass plates suitably screwed 
 to the sides of the trough. The top is closed with a square 
 brass lid, also secured in place with bolts. To this is screwed a 
 vertical condenser, the purpose of which is to liquefy all escap- 
 ing vapor and to return it to the trough. 
 
 The condenser also carries the slide of an agitator or stirring 
 device for equalizing the temperature of any liquid in the 
 trough. 
 
 Temperatures may be read off on the thermometer inserted 
 through and supported by the lid. As is seen, the trough is 
 very solidly put together. It could, if necessary, resist great ex- 
 ternal pressures or be used for experiments in vacua. The glass 
 plates were not fastened with red -lead cement, as is usually 
 done, but the hermetic seal was made by aid of thick plates of 
 vulcanized rubber. I cannot recommend this adjustment too 
 highly, as it is more convenient and more quickly put together 
 than a red-lead joint and much less liable to break the plate- 
 glass windows throughout the limits of temperature within 
 which india-rubber can be employed. With water at 100 this 
 method of sealing leaves nothing to be desired. 
 
 The stem of the manometer of crystal glass passes through 
 the bottom of the trough. The joint is easily made by aid of a 
 tubulure and a perforated cork sliding on the stem. It may 
 also be made with a stuffing-box. In the actual experiments I 
 prefer the first method, which is more simple and gives a good 
 hermetic joint when the necessary precautions are taken, the 
 stem of glass being made to pass through exactly at the centre 
 of the tubulure which holds the cork. The trough, being ad- 
 justable by aid of double nuts on the columns, easily admits of 
 any desirable change of position. One of the columns carries 
 
 18 
 
THE LAWS OF GASES 
 
 a movable ring-burner, through the centre of which the stem 
 of the manometer passes. The crown of flame thus obtained 
 suffices to heat the liquid in the trough to any required de- 
 gree. 
 
 The two parts of the machine are connected by a short 
 tube of steel. The apparatus on the left communicates with 
 the mercury pump mentioned in my first memoir through a 
 somewhat longer piece of the same steel tubing. As the 
 pump has been already described, it needs no further consid- 
 eration here. 
 
 The two couplings or stopcocks seen near the bottom of the 
 apparatus on the left of the figure serve to put into commu- 
 nication different parts of the apparatus, either with them- 
 selves or with the pump, or to interrupt these communications. 
 There is still a third coupling in the extreme left of the figure, 
 but this is not essential in the actual experiments. 
 
 The whole apparatus is fixed to a heavy block of wood by aid 
 of flanges of iron, which I have omitted in the figure. The 
 wooden block in turn is secured to a truck with four rollers of 
 cast-iron ; this allows an easy motion of the whole apparatus, 
 whose weight is quite considerable. Four strong levelling 
 screws were provided for adjusting the stems of the manometers 
 vertically, giving to the whole mechanism additional stability. 
 
 METHOD OF EXPERIMENTATION 
 
 Having partially filled the apparatus with pure and dry 
 mercury, the nitrogen manometer is first installed, and there- 
 after the second manometer provided with its trough. As the 
 latter piece is very heavy, it would be difficult to adjust it man- 
 ually without accident. I therefore had a double differential 
 pulley attached to the ceiling of my laboratory, permitting me 
 to accomplish this operation easily and without danger. Hav- 
 ing completed the adjustment of the apparatus, mercury is 
 injected by the pump until this liquid shows itself in the 
 steins of the manometers. The stopcock on the left is now 
 closed, while additional pressure is applied through the small 
 hand-wheel, the stopcock on the right being left open. 
 
 To begin the measurements, the water in the trough is 
 heated to the temperature selected, and the necessary con- 
 stancy of temperature is maintained by suitably regulating 
 
 19 
 
 UNIVERSITY ] 
 
MEMOIRS ON 
 
 the flow of gas and the distance of the burner from the 
 bottom of the trough. This operation unfortunately is often 
 very prolonged, particularly at the higher temperatures. Dur- 
 ing the whole time the stirring device must be kept in uni- 
 form action. 
 
 When constancy of temperature has been reached, a heavy 
 table of wood is placed facing the apparatus, and two telescopic 
 sights, fixed to the table, are directed to the meniscuses in 
 the two manometers respectively. Thereupon an assistant, by 
 means of the hand-wheel, brings the mercury successively on 
 the division lines of the nitrogen manometer corresponding 
 to the pressures calculated in advance. The observer at the 
 telescopes registers the indications of the two manometers 
 simultaneously with those of the thermometer of the trough 
 and of the jacket of water circulating around the nitrogen 
 manometer. 
 
 As to the latter, observation is made very simply by placing 
 a white screen behind the tube, and always bringing the base 
 of the meniscus upon a division mark of the scale. To read 
 the other manometer, a luminous background, preferably the 
 ground-glass globe of a gas-lamp, is placed at some distance 
 behind the posterior window. The reading of the summit of 
 the meniscus is then observed, well marked by its demarcation 
 from the bright field. In estimating volumes with the aid of 
 a prepared calibration-table, allowance is made for this differ- 
 ence of positions of the meniscuses in the readings. 
 
 METHOD OF CALCULATION 
 
 The experiments which I have made with the different gases 
 are all comprised between 30 and 420 atmospheres, and between 
 atmospheric temperatures and 100 C. 
 
 Each gas was studied in two series of observations. With 
 the first manometer the experiments were carried as far as 100 
 or 130 atmospheres ; with the second I proceeded from 100 or 
 130 atmospheres as far as 420 atmospheres. In this way too 
 great a reduction of the volume of gas is avoided. 
 
 The measurement of pressure given by the nitrogen manom- 
 eter was also carried out with two pieces of apparatus for like 
 reasons. 
 
 This procedure renders the measurement of volume more 
 
 20 
 
THE LAWS OF GASES 
 
 exact, but it has the drawback of presenting difficulties in 
 recording the indications of the two manometers and in reduc- 
 ing them to a single series. I made this reduction by two dif- 
 ferent methods, corroborating them as I shall indicate below. 
 
 The curves representing the results have been constructed as 
 follows : the abscissas are laid oil proportional to the pressures, 
 millimetres of length corresponding to meters of mercury; the 
 lengths of the ordinates are proportional to the corresponding 
 values of the products pv of pressure and volume. 
 
 All the isotherms for the same gas at the different tempera- 
 tures refer to the same gaseous mass ; in other words, the ma- 
 nometers, after once being charged with a given gas, were used 
 in the experiments throughout all temperatures without taking 
 the apparatus apart. To record these families of curves as a 
 whole, I made use of the following two procedures : Consider 
 any particular curve. Supposing that the first manometer 
 has furnished the products pv as far as 130 atmospheres, for 
 example, and the second as far as 120 atmospheres, deduce 
 from the curve constructed up to 130 atmospheres the value 
 of pv at 120 atmospheres. All the numbers furnished by the 
 vsecond manometer are now multiplied by the ratio of the value 
 of pv at 120 atmospheres taken from the first curve to that 
 of the same product furnished by the second manometer at 
 the same pressure. This factor, once calculated, is sufficient to 
 co-ordinate the relative curves at all temperatures, on condi- 
 tion, let it be well understood, that the series which are thus 
 co-ordinated have been made with each manometer at exactly 
 the same temperature. These circumstances were always real- 
 ized to about 1 C., and the coefficient calculated for one of the 
 curves has always made the others agree. To insure greater 
 accuracy I computed the coefficient for all the temperatures 
 and selected the mean value. Thereafter I proceeded as fol- 
 lows : Suppose the gas introduced successively into the two 
 manometers rigorously at the same temperatures and at the 
 same pressure. It would then obviously be sufficient to mul- 
 tiply all the products pv furnished by the second manometer 
 by the ratio of the total volume of the first manometer to that 
 of the second. In reality, however, it was necessary to make 
 a small correction, due to the difference of temperatures and 
 of pressures at which the manometers were charged; but this 
 correction was in all cases very small. The coefficients deter- 
 
 21 
 
MEMOIRS ON 
 
 mined in this way agreed with sufficient accuracy with those 
 determined by the first procedure. They were usually found 
 to be equal to about one per cent., and the mean was taken. 
 Frequently the agreement was even within these limits. 
 
 Finally the curves drawn to the scale which I have given 
 above were reduced to one-third of their original dimensions, 
 which far exceeded the usual size for publication. 
 
 The observations furnished at the nitrogen manometer were 
 reduced in the following way : A table of products pv was 
 first prepared by the aid of my earlier researches, in which the 
 initial volume is considered identical with that of the manom- 
 eter, and the- initial pressure that under which it was charged. 
 Therewith a large curve was constructed by laying oif volumes 
 along the abscissas and the values of pv along the ordinates. 
 From this I deduced the values of pv for the volumes corre- 
 sponding to the scale marks on the nitrogen manometer, up to 
 which the mercury meniscus was forced. Dividing these val- 
 ues by the corresponding volumes deduced from the tables of 
 calibration, the pressure-values sought are obtained. Thus it 
 is supposed that the reading is made at the same temperature 
 as that at- which the manometer was charged at normal press- 
 ure. Hence the correction relative to the difference of tem- 
 perature is always very small. I have also computed the 
 pressures by another method, which gave me essentially the 
 same results. To corroborate the whole I placed the two ni- 
 trogen manometers simultaneously upon the pressure appara- 
 tus, and I thus found that throughout the coincident part of 
 their registry i. e., between about 100 and 130 atmospheres 
 they gave the same results to about half an atmosphere. 
 
 It has just been shown that in making the calculations 
 needed for joining the curves it is necessary to know at what 
 temperature and at what pressure the manometers were charged 
 with gas. The experiments were so conducted that the small 
 cylinder which ends off the reservoirs of the manometers be- 
 low was submerged in mercury at the moment at which its 
 pressure and its temperature were identical with that of the 
 atmosphere, although communication with the gas supply 
 had not yet been cut off. While the small cylinder was thus 
 plunged in the mercury bath, it was provided with a small 
 iron thimble, kept in place by suspension from two springs. 
 In this way the manometer could,, be removed or placed upon 
 
 22 
 
THE LAWS OF GASES 
 
 the apparatus, the efflux point remaining plunged in the mer- 
 cury within the thimble. 
 
 As a general thing, three series of operations were made with 
 each gas and with each manometer. Having thus established 
 the accordance of a large number of series, I selected the one 
 which seemed to have been made under the most satisfactory 
 conditions. 
 
 I took every feasible precaution to have the gases as pure, as 
 free from air, and as dry as possible. For the case of carbon 
 dioxide, in particular, the gas was tested even in the manometer 
 at the end of the experiments. The results given below refer 
 to a gas which left a residue of only 5 parts in lt)00 in the lower- 
 pressure manometer and 2 parts in 1000 in the other. All the 
 gases, without exception, were first dried in concentrated sul- 
 phuric acid, thereafter in a desiccator filled with broken glass 
 mixed with anhydrous phosphoric acid. 
 
 NUMERICAL RESULTS 
 
 The numerical results contained in the following tables were* 
 obtained from the curves which have already been discussed. 
 For ethylene and carbon dioxide, in which the variations of 
 pressure are exceedingly abrupt, I have given the values of 
 pv in intervals from 10 to 10 meters of mercury ; for the other 
 gases, in intervals of x>0 meters only. The first horizontal row 
 shows the temperatures at which the observations were made. 
 The corresponding pressures are contained in the first vertical 
 column. 
 
 In case of marsh gas (methane) data are given only up to- 
 300 atmospheres. This gas was actually studied in certain 
 series as far as 420 atmospheres, like the others ; but an error 
 appeared in the values of the coefficient for co-ordinating these 
 curves which increased to more than three per cent., and which 
 I have not been able to explain to my own satisfaction. I 
 therefore prefer to give the data of the first series only, which 
 showed sufficient accordance throughout. 
 
MEMOIRS ON 
 
 VALUES OF pv FOR NITROGEN 
 
 Meters, Hg. 
 
 17.7 
 
 30.1 
 
 50.4 
 
 75.5 
 
 100.1 
 
 30 
 
 2745 
 
 2875 
 
 3080 
 
 3330 
 
 3575 
 
 40 
 
 2740 
 
 2865 
 
 3085 
 
 3340 
 
 3580 
 
 60 
 
 2740 
 
 2875 
 
 3100 
 
 3360 
 
 3610 
 
 80 
 
 2760 
 
 2895 
 
 3125 
 
 3400 
 
 3650 
 
 100 
 
 2790 
 
 2930 
 
 3170 
 
 3445 
 
 3695 
 
 120 
 
 2835 
 
 2985 
 
 3220 
 
 3495 
 
 3755 
 
 140 
 
 890 
 
 3040 
 
 3275 
 
 3550 
 
 3820 
 
 1(50 
 
 2950 
 
 3095 
 
 3335 
 
 3615 
 
 3880 
 
 180 
 
 3015 
 
 3150 
 
 3390 
 
 3675 
 
 3950 
 
 200 
 
 3075 
 
 3220 
 
 3465 
 
 3750 
 
 4020 
 
 220 
 
 3140 
 
 3285 
 
 3530 
 
 3820 
 
 4090 
 
 240 
 
 3215 
 
 3360 
 
 3610 
 
 3895 
 
 4165 
 
 260 
 
 3290 
 
 3440 
 
 3685 
 
 3975 
 
 4240 
 
 280 
 
 3370 
 
 3520 
 
 3760 
 
 4050 
 
 4320 
 
 300 
 
 3450 
 
 3600 
 
 3840 
 
 4130 
 
 4400 
 
 320 
 
 3525 
 
 3675 
 
 3915 
 
 4210 
 
 4475 
 
 VALUES OF pv FOR HYDROGEN 
 
 Meters, Hg. 
 
 17.7 
 
 40.4 
 
 60.4 
 
 81.1 
 
 100.1 
 
 30 
 
 2830 
 
 3045 
 
 3235 
 
 3430 
 
 3610 
 
 40 
 
 2850 
 
 3065 
 
 3240 
 
 3445 
 
 3625 
 
 60 
 
 2885 
 
 3110 
 
 3295 
 
 3500 
 
 3680 
 
 80 
 
 2935 
 
 3155 
 
 3340 
 
 3550 
 
 3725 
 
 100 
 
 2985 
 
 3200 
 
 3400 
 
 3620 
 
 3780 
 
 120 
 
 3040 
 
 3255 
 
 3455 
 
 3665 
 
 3830 
 
 140 
 
 3080 
 
 3300 
 
 3500 
 
 3710 
 
 3880 
 
 160 
 
 3135 
 
 3360 
 
 3560 
 
 3775 
 
 3945 
 
 180 
 
 3185 
 
 3420 
 
 3620 
 
 3830 
 
 4010 
 
 200 
 
 3240 
 
 3465 
 
 3685 
 
 3870 
 
 4055 
 
 220 
 
 3290 
 
 3520 
 
 3725 
 
 3930 
 
 4110 
 
 240 
 
 3340 
 
 3570 
 
 3775 
 
 3980 
 
 4160 
 
 260 
 
 3400 
 
 3625 
 
 3830 
 
 4040 
 
 4220 
 
 280 
 
 3450 
 
 3675 
 
 3880 
 
 4090 
 
 4275 
 
 300 
 
 3500 
 
 3730 
 
 3935 
 
 4140 
 
 4325 
 
 320 
 
 3550 
 
 3780 
 
 3990 
 
 4200 
 
 4385 
 
< 
 
 1 T ISITY] 
 
 THE LAWS OF GASl^^i 
 
 MARSH GAS (METHANE) 
 
 Meters, Hg. 
 
 14.7 
 
 29.5 
 
 40.6 
 
 60.1 
 
 79.8 
 
 100.1 
 
 TO 
 
 2580 
 
 2745 
 
 2880 
 
 HI 00 
 
 
 
 *J \J 
 
 40 
 
 2515 
 
 /V i TTJ 
 
 2685 
 
 >vOOV/ 
 
 2830 
 
 tJ X \J\J 
 
 3060 
 
 3290 
 
 3505 
 
 i 60 
 
 2400 
 
 2590 
 
 2735 
 
 2995 
 
 3230 
 
 3460 
 
 80 
 
 2315 
 
 2515 
 
 2675 
 
 2950 
 
 3195 
 
 3440 
 
 100 
 
 2275 
 
 2480 
 
 2640 
 
 2935 
 
 3180 
 
 3435 
 
 120 
 
 2245 
 
 2465 
 
 2635 
 
 2925 
 
 3180 
 
 3440 
 
 140 
 
 2260 
 
 2480 
 
 2655 
 
 2940 
 
 3190 
 
 3460 
 
 160 
 
 2300 
 
 2510 
 
 2685 
 
 2975 
 
 3220 
 
 3490 
 
 180 
 
 2360 
 
 2560 
 
 2730 
 
 3015 
 
 3260 
 
 3525 
 
 200 
 
 2425 
 
 2615 
 
 2780 
 
 3065 
 
 3305 
 
 3575 
 
 220 
 
 2510 
 
 2690 
 
 2840 
 
 3125 
 
 3360 
 
 3625 
 
 230 
 
 2560 
 
 2730 
 
 2880 
 
 3150 
 
 3385 
 
 3650 
 
 M.IIg. 
 
 16.3 
 
 \ 
 
 20.3 
 
 ALUEf 
 
 30.1 
 
 5 OF j 
 40.0 
 
 PV FO 
 
 50.0 
 
 R ETI 
 
 60.0 
 
 IYLEN 
 70.0 
 
 E 
 79.9 
 
 89.9 
 
 100.0 
 
 25 
 
 01 /LA 
 
 991 ^ 
 
 9360 
 
 
 
 
 
 
 
 
 /CO 
 
 30 
 
 /V J-TTV/ 
 
 1950 
 
 v/v'-L tJ 
 
 2055 
 
 4vO vVr 
 
 2220 
 
 2410 
 
 2580 
 
 2715 
 
 2865 
 
 2970 
 
 3090 
 
 3225 
 
 40 
 
 1350 
 
 1700 
 
 1900 
 
 2145 
 
 2335 
 
 2510 
 
 2675 
 
 2825 
 
 2960 
 
 3110 
 
 50 
 
 850 
 
 1075 
 
 1540 
 
 1860 
 
 2100 
 
 2315 
 
 2490 
 
 2670 
 
 2825 
 
 2980 
 
 60 
 
 810 
 
 900 
 
 1190 
 
 1535 
 
 1875 
 
 2100 
 
 2310 
 
 2500 
 
 2680 
 
 2860 
 
 70 
 
 880 
 
 945 
 
 1110 
 
 1340 
 
 1675 
 
 1920 
 
 2150 
 
 2365 
 
 2560 
 
 2740 
 
 80 
 
 975 
 
 1030 
 
 1130 
 
 1285 
 
 1535 
 
 1780 
 
 2015 
 
 2240 
 
 2450 
 
 2640 
 
 90 
 
 1065 
 
 1115 
 
 1195 
 
 1325 
 
 1510 
 
 1710 
 
 1930 
 
 2160 
 
 2375 
 
 2565 
 
 100 
 
 1150 
 
 1200 
 
 1275 
 
 1380 
 
 1535 
 
 1690 
 
 1895 
 
 2105 
 
 2335 
 
 2515 
 
 110 
 
 1240 
 
 1280 
 
 1360 
 
 1460 
 
 1590 
 
 1725 
 
 1915 
 
 2705 
 
 2310 
 
 2490 
 
 120 
 
 1325 
 
 1370 
 
 1440 
 
 1540 
 
 1660 
 
 1780 
 
 1950 
 
 2115 
 
 2305 
 
 2470 
 
 130 
 
 1415 
 
 1455 
 
 1525 
 
 1620 
 
 1725 
 
 1840 
 
 2000 
 
 2150 
 
 2320 
 
 2480 
 
 140 
 
 1505 
 
 1540 
 
 1610 
 
 1700 
 
 1800 
 
 1910 
 
 2060 
 
 2190 
 
 2350 
 
 2505 
 
 150 
 
 1590 
 
 1625 
 
 1690 
 
 1785 
 
 1880 
 
 1990 
 
 2125 
 
 2250 
 
 2390 
 
 2540 
 
 160 
 
 1680 
 
 1715 
 
 1780 
 
 1865 
 
 1960 
 
 2070 
 
 2195 
 
 2310 
 
 2445 
 
 2585 
 
 170 
 
 1770 
 
 1800 
 
 1860 
 
 1950 
 
 2045 
 
 2145 
 
 2265 
 
 2375 
 
 2505 
 
 2640 
 
 180 
 
 1855 
 
 1890 
 
 1945 
 
 2035 
 
 2130 
 
 2225 
 
 2340 
 
 2450 
 
 2565 
 
 2700 
 
 190 
 
 1940 
 
 1975 
 
 2030 
 
 2120 
 
 2210 
 
 2310 
 
 2415 
 
 2525 
 
 2635 
 
 2760 
 
 200 
 
 2030 
 
 2065 
 
 2115 
 
 2200 
 
 2290 
 
 2390 
 
 2490 
 
 2600 
 
 2715 
 
 2835 
 
 210 
 
 2110 
 
 2145 
 
 2200 
 
 2285 
 
 2375 
 
 2470 
 
 2565 
 
 2680 
 
 2790 
 
 2910 
 
 220 
 
 2195 
 
 2225 
 
 2280 
 
 2370 
 
 2460 
 
 2550 
 
 2650 
 
 2760 
 
 2865 
 
 2975 
 
 230 
 
 2280 
 
 2315 
 
 2370 
 
 2460 
 
 2540 
 
 2635 
 
 2730 
 
 2835 
 
 2940 
 
 3050 
 
 240 
 
 2360 
 
 2395 
 
 2450 
 
 2540 
 
 2625 
 
 2720 
 
 2810 
 
 2910 
 
 3015 
 
 3125 
 
 250 
 
 2445 
 
 2480 
 
 2540 
 
 2625 
 
 2710 
 
 2800 
 
 2890 
 
 2990 
 
 3090 
 
 3200 
 
 260 
 
 2530 
 
 2560 
 
 2625 
 
 2710 
 
 2790 
 
 2880 
 
 2980 
 
 3075 
 
 3175 
 
 3275 
 
 270 
 
 2610 
 
 2640 
 
 2710 
 
 2790 
 
 2875 
 
 2965 
 
 3060 
 
 3150 
 
 3240 
 
 3345 
 
 "280 
 
 2695 
 
 2725 
 
 2790 
 
 2875 
 
 2960 
 
 3045 
 
 3140 
 
 3225 
 
 3320 
 
 3420 
 
 290 
 
 2780 
 
 2810 
 
 2875 
 
 2960 
 
 3040 
 
 3125 
 
 3220 
 
 3310 
 
 3400 
 
 3490 
 
 300 
 
 2860 
 
 2890 
 
 2960 
 
 3040 
 
 3125 
 
 3215 
 
 3300 
 
 3380 
 
 3470 
 
 3560 
 
 310 
 
 2945 
 
 2975 
 
 3040 
 
 3125 
 
 3210 
 
 3290 
 
 3385 
 
 3465 
 
 3550 
 
 3635 
 
 320 
 
 3035 
 
 3065 
 
 3125 
 
 3200 
 
 3285 
 
 3375 
 
 3470 
 
 3545 
 
 3625 
 
 3710 
 
MEMOIRS ON 
 
 M.Hg. 
 
 VAl 
 
 18.2 
 
 LUES 
 35.1 
 
 OF pv 
 
 40.2 
 
 FOR 
 
 50.0 
 
 CARBC 
 60.0 
 
 )N DIOXIDE 
 70.0 80.0 
 
 90.2 
 
 100.0 
 
 30 
 
 Liquid 
 
 2360 
 
 2460 
 
 2590 
 
 2730 
 
 2870 
 
 2995 
 
 3120 
 
 3225 
 
 40 
 
 a 
 
 2065 
 
 2195 
 
 2370 
 
 2535 
 
 2700 
 
 2840 
 
 2985 
 
 3105 
 
 50 
 
 tf 
 
 1725 
 
 1900 
 
 2145 
 
 2330 
 
 2525 
 
 2685 
 
 2845 
 
 2980 
 
 60 
 
 a 
 
 1170 
 
 1500 
 
 1860 
 
 2115 
 
 2340 
 
 2530 
 
 2705 
 
 2860 
 
 70 
 
 
 
 725 
 
 950 
 
 1530 
 
 1890 
 
 2155 
 
 2380 
 
 2570 
 
 2750 
 
 80 
 
 625 
 
 750 
 
 825 
 
 1200 
 
 1650 
 
 1975 
 
 2225 
 
 2440 
 
 2635 
 
 90 
 
 685 
 
 810 
 
 865 
 
 1080 
 
 1430 
 
 1775 
 
 2075 
 
 2315 
 
 2530 
 
 100 
 
 760 
 
 870 
 
 920 
 
 1065 
 
 1315 
 
 1630 
 
 1940 
 
 2200 
 
 2425 
 
 110 
 
 825 
 
 930 
 
 980 
 
 1090 
 
 1275 
 
 1550 
 
 1845 
 
 2105 
 
 2325 
 
 120 
 
 j 890 
 
 995 
 
 1045 
 
 1140 
 
 1285 
 
 1510 
 
 1775 
 
 2030 
 
 2260 
 
 130 
 
 955 
 
 1060 
 
 1115 
 
 1190' 
 
 1315 
 
 1505 
 
 1735 
 
 1980 
 
 2190 
 
 140 
 
 1020 
 
 1120 
 
 1175 
 
 1250 
 
 1360 
 
 1525 
 
 1715 
 
 1950 
 
 2160 
 
 150 
 
 1080 
 
 1180 
 
 1235 
 
 1310 
 
 1415 
 
 1560 
 
 1725 
 
 1945 
 
 2135 
 
 160 
 
 1145 
 
 1250 
 
 1300 
 
 1370 
 
 1465 
 
 1600 
 
 1745 
 
 1960 
 
 2130 
 
 170 
 
 1210 
 
 1310 
 
 1360 
 
 1430 
 
 1520 
 
 1645 
 
 1780 
 
 1975 
 
 2135 
 
 180 
 
 1275 
 
 1375 
 
 1410 
 
 1485 
 
 1580 
 
 1700 
 
 1825 
 
 2000 
 
 2150 
 
 190 
 
 1340 
 
 1440 
 
 1480 
 
 1550 
 
 1645 
 
 1760 
 
 1875 
 
 2035 
 
 2180 
 
 200 
 
 1405 
 
 1500 
 
 1550 
 
 1615 
 
 1705 
 
 1810 
 
 1930 
 
 2075 
 
 2215 
 
 210 
 
 1470 
 
 1565 
 
 1610 
 
 1675 
 
 1765 
 
 1870 
 
 1980 
 
 2120 
 
 2250 
 
 220 
 
 1530 
 
 1625 
 
 1670 
 
 1740 
 
 1825 
 
 1925 
 
 2040 
 
 2160 
 
 2290 
 
 230 
 
 1590 
 
 1690 
 
 1730 
 
 1800 
 
 1890 
 
 1990 
 
 2090 
 
 2210 
 
 2340 
 
 240 
 
 1650 
 
 1750 
 
 1790 
 
 1865 
 
 1950 
 
 2045 
 
 2150 
 
 2260 
 
 2390 
 
 250 
 
 1710 
 
 1815 
 
 1855 
 
 1925 
 
 2010 
 
 2100 
 
 2205 
 
 2320 
 
 2435 
 
 260 
 
 1770 
 
 1870 
 
 1920 
 
 1985 
 
 2070 
 
 2165 
 
 2265 
 
 2375 
 
 2490 
 
 270 
 
 1830 
 
 1935 
 
 1975 
 
 2050 
 
 2130 
 
 2220 
 
 2320 
 
 2435 
 
 2540 
 
 280 
 
 1890 
 
 2000 
 
 2040 
 
 2110 
 
 2190 
 
 2285 
 
 2380 
 
 2490 
 
 2600 
 
 290 
 
 1950 
 
 2060 
 
 2100 
 
 2170 
 
 2260 
 
 2340 
 
 2440 
 
 2550 
 
 2655 
 
 300 
 
 2010 
 
 2120 
 
 2160 
 
 2235 
 
 2320 
 
 2405 
 
 2500 
 
 2605 
 
 2715 
 
 310 
 
 2070 
 
 2180 
 
 2220 
 
 2300 
 
 2375 
 
 2460 
 
 2560 
 
 2660 
 
 2765 
 
 320 
 
 2135 
 
 2240 
 
 2280 
 
 2360 
 
 2440 
 
 2525 
 
 2620 
 
 2725 
 
 2830 
 
 The curves given in figures 2, 3, 4, 5, 6, represent these results 
 comprehensively. In those relative to nitrogen, to hydrogen, 
 and to marsh gas a part of the ordinate lengths has been sup- 
 pressed. It is therefore necessary to reproduce this inferential- 
 ly with the aid of the numbers given at the origin. 
 
 EXAMINATION AND DISCUSSION OF THE RESULTS 
 
 An inspection of the curves shows at once that the families 
 may be referred to two extreme and to certain intermediate 
 types. For hydrogen all the lines are appreciably parallel and 
 
 26 
 
THE LAWS OF GASES 
 
 straight at all the temperatures at which experiments were 
 made. This invariability in the form of the curves seems 
 to indicate that this gas has reached a limiting state charac- 
 terized by their direction. At all the temperatures which I 
 investigated the values of pv increase in their variation with 
 pressure. 
 
 Carbon dioxide and ethylene form the contrasting type. The 
 products pv at first decrease very rapidly, reach a minimum, 
 
 20 40 60 80 100 120 140 160 180 200 220 240 260 280 
 
 FIG. 2. ISOTHERMS (pv) FOR NITROGEN 
 
 and thereafter increase indefinitely. These variations of pv, 
 very rapid at temperatures near the critical point, show a 
 marked diminution when temperature rises. The point of the 
 curve at which the ordinate is a minimum moves regularly 
 away from the origin, and the locus traced comes out very clearly 
 on inspection of the curves. The minimum seems to move away 
 from the origin less rapidly after passing a certain temperature ; 
 after which it apparently retrogrades. At least, this takes place 
 in marsh gas and nitrogen. Now these gases which constitute 
 the intermediate type are at like temperatures much more dis- 
 tant, from their critical state than ethylene or carbon dioxide. 
 For the case of nitrogen and marsh gas the displacement of the 
 minimum ordinate appears much less sharply defined than for 
 the other gases, for the reason that when curvature diminishes, 
 the position of this ordinate is much more difficult to determine 
 sharply. I subjoin a table for carbon dioxide and ethylene, 
 
 27 
 
MEMOIRS ON 
 
 showing at what pressure in meters of mercury the ordinate is 
 a minimum at different temperatures : 
 
 CARBON DIOXIDE 
 
 ETHYLENE 
 
 
 
 
 
 16.3 
 
 55" 
 
 
 
 
 
 20.3 
 
 60 
 
 35.1 
 
 70* 
 
 30.1 
 
 70 
 
 40.2 
 
 80 
 
 40.0 
 
 80 
 
 50.0 
 
 98 
 
 '50.0 
 
 88 
 
 60.0 
 
 115 
 
 60.0 
 
 95 
 
 \70.0 
 
 130 
 
 70.0 
 
 100 
 
 80.0 
 
 140 
 
 79.9 
 
 105 
 
 90.2 
 
 150 
 
 89.9 
 
 115 
 
 100.0 
 
 160 
 
 100.0 
 
 120 
 
 The curves for carbon dioxide and ethylene may advan- 
 tageously be considered by themselves for the time being ; be- 
 cause of the larger variations of compressibility involved, they 
 
 44 
 
 42 
 
 26 
 
 40 
 
 38 
 
 36 
 
 34 
 
 32 
 
 ,30 
 
 28 i 
 
 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 
 
 FIG. 3. ISOTHERMS (pv) FOR HYDROGEN 
 
 are more suitable than the others for the demonstration of the 
 general laws of these variations. Let the curves for carbon 
 dioxide be taken first. It is obvious at the outset that at tem- 
 peratures in the neighborhood of the critical point the initial 
 branches of the curves, or those which precede the minimum 
 ordinate, are concave towards the axis of pressure. The con- 
 
 28 
 
THE LAWS OF GASES 
 
 cavity is well marked, and appears to be prolonged quite into 
 the region of small pressures. This is indicated by the dotted 
 lines which represent the phenomenon approximately, at press- 
 ures lower than those at which the experiments began. 
 
 To construct these parts of the curve I simply determined 
 
 20 '40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 
 FIG. 4. ISOTHERMS (pv) FOR ETHYLENE 
 
 the point of departure corresponding to normal pressure, which 
 was found without difficulty, since I knew the volume of carbon 
 dioxide for the particular pressure and temperature at which 
 the manometer was charged with gas. From this I deduced 
 the volume occupied by the gas, and consequently the value of 
 
MEMOIRS ON 
 
 pv, at the same pressure for all the temperatures, in virtue of 
 the values of the coefficient of expansion of carbon dioxide, 
 given a long time ago in my own papers, for temperatures 
 between and 100 and under normal pressure. Thereupon I 
 joined the points of departure so obtained with the first points 
 of the continuous curves, allowing myself to be guided by their 
 
 20 40 60 80 100 120 140 160 180 200 220 240 260 230 300 320 
 
 YIG. 5. ISOTHERMS (pv) FOR CARBON DIOXIDE 
 
 general trend. Similar dotted lines were drawn for nitrogen 
 and hydrogen, but not for ethylene and methane, since I lacked 
 data as to their dilatation. 
 
 To return from this digression to the general form of the 
 curves, I may point out that the concavity observed in the 
 initial branches which is presented in the case of ethylene, 
 
 30 
 
THE LAWS OF GASES 
 
 occurs also, I might almost say a fortiori, in the results which 
 Regnault investigated as far as 28 atmospheres. In fact, these 
 data were obtained at temperatures lower than those from which 
 I started i. e., lower than 35 for carbon dioxide. 
 
 The concavity specified vanishes pretty rapidly when tempera- 
 ture rises. At 50 0. it is no longer apparent, and the curve only 
 presents the convexity which produces the minimum of pv. 
 
 For gases other than ethylene and carbon dioxide, the con- 
 cavity has entirely disappeared even at ordinary temperatures. 
 This form of curve for the lower pressures, for the moment at 
 
 36 
 
 32 
 
 30 
 
 28 
 
 26 
 
 24 
 
 22 
 
 20 40 60 80 "100 120 140 '160 180 230 220 240 
 
 FIG. 6. ISOTHERMS (pv) FOR MARSH GAS 
 
 least, does not command much attention ; but it is quite dif- 
 ferent in those parts of the curves which follow the minimum 
 ordinate, and throughout which pv increases indefinitely. For 
 temperatures in the neighborhood of the critical point, the 
 curve turns rapidly after passing the ordinate in question, and 
 changes almost at once into a line which is very nearly straight. 
 Some points seem to indicate traces of concavity, so vaguely, 
 however, as to be referable to errors of observation. 
 
 As temperature rises the convexity of the curves diminishes 
 very rapidly, and the general aspect of the families of curves 
 shows an unmistakable tendency to slope upward and to change 
 to straight lines throughout their extent. The occurrence of 
 minimum ordinates thus gradually ceases. 
 
 31 
 
MEMOIRS ON 
 
 True, this tendency is indicated clearly only in the isotherms 
 of carbon dioxide and of ethylene. If, however, one calls to 
 mind that hydrogen is at ordinary temperatures in a thermal 
 state, which the two gases specified reach at very much higher 
 temperatures ; that for hydrogen the transformation in ques- 
 tion is actually complete at ordinary temperatures, continuing 
 in the same sense up to 100 without showing the slightest 
 trace of any superimposed deformation ; if, finally, one adds 
 the evidence obtained from the curves for methane and nitro- 
 gen which make up the intermediate type, then the general 
 features of these gaseous phenomena become strikingly appar- 
 ent. Indeed, I would insist on this point of view (the conse- 
 quences of which will be shown below), that not only do the 
 curves straighten out for all gases in such a way as to reproduce 
 the case of hydrogen at sufficiently high temperatures i.e., 
 in a way to present values of pv continually increasing with 
 pressure but that they really tend to become straight lines 
 throughout their whole extent. 
 
 For hydrogen the occurrence of straight isotherms is as 
 completely verified as the accuracy of the experiments permits 
 up to 100 atmospheres about and from ordinary temperatures 
 onward. At smaller pressures, a trace of concavity seems still 
 to cling to the curves. This is much less discernible at 100, 
 if it be not altogether wiped out. 
 
 The concavity of the curves for nitrogen is clearly marked 
 at ordinary temperatures, but it is much less accentuated at 
 100, where the rectilinear portions are already apparent. 
 
 Another fact not less important (as will appear below) is this, 
 that the curves in their rectilinear parts are nearly parallel ; 
 parallel in such a way, moreover, that to obtain the general 
 direction of these lines a characteristic for each gas it is 
 sufficient to construct one of them near the critical point. 
 Under critical conditions the lines become straight almost 
 immediately after leaving the minimum ordinate. Neverthe- 
 less, it would be hazardous to affirm that these lines are abso- 
 lutely parallel ; they seem rather to merge gradually into 
 straight lines, being asymptotic to a direction which differs 
 very little in all the cases for the portion already sensibly 
 straight in the curves constructed. 
 
 The endeavor must now be made to unravel general laws 
 relative to the variation of compressibility with temperature. 
 
 32 
 
THE LAWS OF GASES 
 
 AVe have seen that for each gas there exists a temperature 
 beyond which pv increases continually with pressure. It is, 
 however, inaccurate to state that with increasing temperature 
 the gas continues to diverge more and more seriously from the 
 law of Mariotte, in the sense of being less compressible. The 
 
 contrary is the fact. Let the values of the ratio -^r-, be examined 
 
 p v 
 
 between the limits p and p' of pressure and at different tem- 
 peratures. It follows from the parallelism of the lines that 
 in passing from a given temperature to another higher in the 
 scale the values of pv and p'v' increase by the same quantity. 
 Hence the value of the ratio increases, since it is smaller than 
 one. 
 
 All this is clearly shown in the following table containing 
 
 7)V 
 
 values of - between 100 meters and 320 meters of pressure 
 p v 
 
 and at different temperatures: 
 
 HYDROGEN 
 
 C. RATIO V?-, 
 
 pv 
 
 17.7 0.830 
 
 40.4 838 
 
 60.4 ' 845 
 
 80.1 853 
 
 100.1 . .856 
 
 Thus for increasing temperatures the gas expands more in 
 accordance with Mariotte J s law, for the simple reason that the 
 constant difference of the products pv and p'v' is added to the 
 greater and greater values of the products. The reason is not 
 that jov tends to become constant, a result which occurs for no 
 gas whatever. 
 
 It is quite certain that, on sufficiently cooling hydrogen, this 
 gas would eventually contract more than the law of Mariotte 
 indicates. On increasing temperature the discrepancy would 
 at first vanish and thereafter change sign. But the divergence, 
 instead of continuing to increase negatively, would reach a 
 maximum value, after which it would begin to approacli unity, 
 as is actually the case in the experiments, 
 c 33 
 
MEMOIRS ON 
 
 Let the family of curves relative to carbon dioxide now be 
 examined : They begin at 35 C. i.e., only a few degrees above 
 
 the critical point. Following the values -,, from degree to 
 
 degree between the pressure limits 100 and 120 meters of mer- 
 cury, for example, we find the ratio smaller than unity at 35, 
 40, and 50. Above 60, on the contrary, the ratio exceeds 
 unity ; after this it evidently again becomes smaller as the 
 temperature continually increases, and finally remains indefi- 
 nitely at a point below this value. Clearly, therefore, the 
 period within which the gas is more compressible than the law 
 of Mariotte asserts may be preceded by a period where it is 
 less so at a lower temperature. The curves also show that a 
 
 1)V 
 
 pressure exists beyond which - L r - l is always smaller than unity, 
 
 whatever be the temperature. If one imagines the locus of the 
 points of minimum ordinates actually constructed, and if the 
 curve has itself a maximum abscissa (I have shown that this is 
 very probable), it is beyond the pressure corresponding to this 
 abscissa that the fact in question becomes manifest. 
 
 Approaching the region of lower pressures one observes simi- 
 larly that a value exists beyond which the primary period cor- 
 
 79?^ 
 
 responding to -; < 1 no longer occurs. The value in ques- 
 tion is the pressure at which the gas liquefies at a temperature 
 very near the critical point. It is the critical pressure. 
 
 All these results are rather complicated, although an inspec- 
 tion of the curves immediately shows them clearly. They may, 
 however, be enunciated in a simpler form. Suppose the family 
 of curves divided into two regions by the curve which is the 
 locus of minimum ordinates. The left-hand area will then 
 
 DV 
 
 comprehend those parts of the curves for which --,--, > 1; in 
 the right-hand area, contrariwise, we shall everywhere have 
 
 ItV *DV 
 
 J - i , < 1. In the first region, -; decreases when temperature 
 
 increases ; in the second the opposite is the case. 
 
 The following table has been computed from the data for 
 carbon dioxide to substantiate these results. It may be 
 observed in passing that in the second region the effect of 
 temperature diminishes whenever pressure increases. 
 
 34 
 
THE LAWS OF GASES 
 
 CARBON DIOXIDE 
 
 TEMP. 
 
 3QX10M 
 
 VA 
 
 LUES OF - 
 
 pv 
 
 200* 
 
 ?V 
 
 140* 20(W 
 
 18.2 (Liq.) 
 
 
 
 
 
 .745 
 
 .726 
 
 .658 
 
 35.1 
 
 3.255 
 
 .833 
 
 .777 
 
 .747 
 
 .670 
 
 40.2 
 
 2.893 
 
 .924 
 
 .783 
 
 .758 
 
 .688 
 
 50.0 " 
 
 1.693 
 
 1.452 
 
 .844 
 
 .774 
 
 .685 
 
 60.0 
 
 1.444 
 
 1.437 
 
 .967 
 
 .797 
 
 .699 
 
 70.0 
 
 1.329 
 
 1.322 
 
 1.069 
 
 .842 
 
 .712 
 
 80.0 " 
 
 1.258 
 
 1.227 
 
 1.131 
 
 .888 
 
 .736 
 
 90.2 
 
 1.214 
 
 1.168 
 
 1.128 
 
 .940 
 
 .761 
 
 100.0 " 
 
 1.172 
 
 1.134 
 
 1.122 
 
 .975 
 
 .782 
 
 The limits of pressure between which ~- ; has been calculated 
 
 are inscribed at the head of the respective vertical columns. 
 We may therefore summarize the role of temperature in its 
 effect upon the compressibility of gases by the following laws : 
 
 1. For pressures lower than the critical pressure and with con- 
 tinually increasing temperature, the divergence from Mariotte's 
 law, positive at first at sufficiently low temperatures, passes 
 through zero and eventually becomes negative. Beyond a certain 
 negative value, however, the discrepancy diminishes indefinitely 
 without changing sign. 
 
 2. For pressures between the critical value and a superior 
 limit peculiar to each gas, the period during which the dis- 
 crepancy is positive is preceded at still lower temperatures by a 
 period for which it is negative, in such a way that the discrepancy 
 changes sign twice. 
 
 #. Beyond the superior limit indicated in the preceding law 
 the discrepancy is negative at all temperatures. It diminishes 
 in general as temperature increases, always excepting those press- 
 ures which are too near the limit specified. In these places the 
 variation is more complicated. 
 
 4. Begond a sufficiently high temperature the law of compressi- 
 bility of a gas is represented by the equation P ( Va) = const., 
 wherein a is the smallest volume to which the gas can be reduced; 
 in other ivords, a is the absolute volume of the constih 
 
 35 
 
 UNIVERSITY 
 
MEMOIRS ON 
 
 The last law virtually states (as will appear below) that 
 beyond a certain sufficiently high temperature all the curves 
 become straight lines. 
 
 It goes without saying that the departure from the law of 
 Mariotte here in question refers to pressures arbitrarily chosen 
 within the limits of pressure indicated by the laws. 
 
 DILATATION OF GASES AT HIGH PRESSURES 
 
 The data which precede are evidently available for the com- 
 putation of the coefficient of expansion of a gas, even though 
 the experiments were not specially directed towards this end. 
 True, results so obtained cannot have a degree of precision 
 comparable with those investigated by the ordinary methods at 
 low pressures ; but the accuracy will nevertheless be sufficient 
 to point out the general features. 
 
 Mere inspection of the families of curves enables us to 
 form a conception of the remarkable variation to which the 
 dilatation of a gas is subject in the neighborhood of the locus 
 of minimum ordinates; above all, at temperatures near the 
 critical point. 
 
 If we reflect that for a given pressure the length of the ordi- 
 nate is at each temperature proportional to the volume of the 
 gas, it follows that the dilatation for each pressure is conse- 
 quently given by the curves. To arrive at the general facts, 
 however, it is necessary to compare the coefficients of mean 
 expansion at different pressures between the sufficiently narrow 
 limits of temperature. It is with this end in view that I have 
 computed the table which is about to follow. 
 
 7j' 2 
 
 The coefficients of expansion inserted are the values of //__//\ 
 
 between the limits of pressure and of temperature indicated. 
 The volumes were deduced from the curves by dividing the 
 ordinates pv by the corresponding pressure. It sufficed for this 
 purpose to take the difference of ordinates corresponding to 
 t and t' degrees at each pressure, to divide this difference by 
 
 fk\^ 1J -/I?? 7? m- 7T 
 
 the inferior ordinate giving ^ or - , and finally to 
 
 pv v 
 
 divide this result by the difference of temperature. 
 
 The data thus obtained for carbon dioxide and ethylene 
 follow : 
 
THE LAWS OF GASES 
 
 Pressure 
 
 CAKB 
 
 18 35 
 
 ON DIOXIDI 
 40o_60 
 
 3 
 60 80 
 
 80 100 
 
 40 Meters 
 
 Liquid 
 
 .0074 
 
 .0058 
 
 .0046 
 
 60 
 
 
 
 .0196 
 
 .0096 
 
 .0052 
 
 80 
 
 .0113 
 
 .0500 
 
 .0176 
 
 .0089 
 
 100 " 
 
 .0072 
 
 .0217 
 
 .0238 
 
 .0135 
 
 120 
 
 .0062 
 
 .0114 
 
 .0151 
 
 .0123 
 
 140 
 
 
 
 .0085 
 
 '.0128 
 
 .0127 
 
 160 
 
 .0043 
 
 .0066 
 
 .0095 
 
 .0108 
 
 180 
 
 
 
 .0056 
 
 .0079 
 
 .0087 
 
 200 
 
 .0039 
 
 .0052 
 
 .0071 
 
 .0072 
 
 220 
 
 
 
 .0048 
 
 .0057 
 
 .0063 
 
 240 
 
 .0033 
 
 .0045 
 
 .0051 
 
 .0056 
 
 260 
 
 
 
 .0040 
 
 .0045 
 
 .0048 
 
 280 
 
 .0029 
 
 .0039 
 
 .0042 
 
 .0046 
 
 300 
 
 
 
 .0038 
 
 .0039 
 
 .0044 
 
 320 
 
 .0025 
 
 .0037 
 
 .0038 
 
 .0040 
 
 ETHYLENE 
 
 Pressure 
 
 20040 
 
 40o_60 
 
 60 80 
 
 80 100 
 
 30 Meters 
 
 .0084 
 
 .0064 
 
 .0046 
 
 .0040 
 
 60 
 
 .0366 
 
 .0178 
 
 .0097 
 
 .0067 
 
 80 
 
 .0121 
 
 .0195 
 
 .0132 
 
 .0088 
 
 100 
 
 .0079 
 
 .0108 
 
 .0121 
 
 .0100 
 
 120 
 
 .0062 
 
 .0075 
 
 .0095 
 
 .0082 
 
 140 
 
 .0048 
 
 .0062 
 
 .0076 
 
 .0068 
 
 160 
 
 .0041 
 
 .0057 
 
 .0061 
 
 .0058 
 
 200 
 
 .0034 
 
 .0043 
 
 .0044 
 
 .0044 
 
 240 
 
 .0030 
 
 .0035 
 
 .0036 
 
 .0034 
 
 280 
 
 .0027 
 
 .0031 
 
 .0030 
 
 .0029 
 
 320 
 
 .0025 
 
 .0027 
 
 .0024 
 
 .0024 - 
 
 If by running along a horizontal column one endeavors to 
 find how the coefficient of expansion varies with temperature 
 at constant pressure, one observes a rather complex result for 
 the values given in the middle of the table, which correspond 
 to* the neighborhood of the locus of minimum ordinates ; but 
 if one considers only the extreme regions, regions which corre- 
 spond to low pressures or to pressures relatively high, it becomes 
 easily manifest that the coefficient diminishes regularly with 
 temperature. Particularly on arriving near the limits of press- 
 
 37 
 
MEMOIRS ON 
 
 lire will it be observed that the expansion is sensibly propor- 
 tional to the interval of temperature. This is the case with 
 hydrogen at all pressures. 
 
 Again, if in a survey of the vertical columns of the tables we 
 endeavor to find the variation of the coefficient of expansion 
 with pressure at a given constant temperature, we encounter a 
 clear-cut law at once. The coefficient is at first seen to increase 
 with pressure up to a maximum value, and thereafter to decrease 
 regularly. This maximum corresponds very nearly to the 
 pressure for which the ordinate is a minimum. If in place of 
 taking the mean coefficient between limits as far apart as 20 
 the temperature interval t' t be more and more diminished, 
 
 the limiting value -j- - will coincide as to the pressure position 
 
 of its maximum with the same pressure which corresponds to 
 the minimum ordinate. 
 
 In proportion as temperature increases, this maximum is less 
 and less marked until it eventually vanishes, as in the case of 
 hydrogen. The following table, drawn up for this gas, shows 
 at the same time that the mean coefficient decreases uniformly 
 when pressure increases. 
 
 HYDROGEN 
 
 Pressure 
 
 17 60 
 
 60 100 
 
 40 Meters 
 100 
 180 
 260 
 320 
 
 .0033 
 .0033 
 .0031 
 .0030 
 
 .0028 
 
 .0029 
 .0028 
 .0027 
 .0025 
 .0024 
 
 I may, therefore, summarize the laws relative to the expan- 
 sion of gases in the following way : 
 
 1. The coefficient of expansion of gases (referred to the unit of 
 volume) increases with pressure up to a maximum value, beyond 
 which it decreases indefinitely. 
 
 2. The pressure corresponding to this maximum coincides in 
 position with the pressure for which the product pv is a minimum. 
 Consequently, at this exceptional point the gas accidentally obey* 
 the law of Mariotte. 
 
 38 
 
THE LAWS OF GASES 
 
 3. For continually increasing temperatures the maximum in 
 question becomes more and more indistinct and finally vanishes. 
 
 COVOLUME ATOMIC VOLUME 
 
 We have seen that for hydrogen the curves obtained are 
 nearly straight lines, and that the same is the case for carbon 
 dioxide and for ethylene throughout a considerable part of the 
 region beyond the minimum ordinate. We have seen further- 
 more that for increasing temperatures the curves tend more 
 and more to become straight lines throughout their whole ex- 
 tent, thus again resembling the phenomenon observed with 
 hydrogen at temperatures above that of the atmosphere. In 
 this case the curves become 
 
 (1) pv a p -j- 1). 
 
 The initial ordinate b being the value of pv at the limit i.e., fora 
 pressure infinitely small, if the laws which we have adduced are 
 true under these conditions. This indeed is a question which 
 has not yet been sufficiently studied and which I shall shortly 
 take up again. We shall therefore regard our inferences limited 
 as to pressures to an interval within which the results present a 
 sufficient degree of certitude. As to hydrogen, I have already 
 stated that for pressures less than 100 atmospheres the line still 
 shows a slight curvature even at 100 0. But it is reasonable to 
 admit that this curvature will quite vanish at temperatures taken 
 high enough, and that the line will become straight at least, 
 above the pressures in the neighborhood of normal pressure. 
 
 The equation (1) may be put in the form 
 
 (*) P (r- a )=b, 
 
 b and a being constants. The result arrived at is therefore 
 this, that at a given temperature the product of the pressure 
 and the volume diminished by a constant quantity does not 
 vary. If furthermore the relation is written 
 
 (j^tf-l, 
 
 it appears that when p = cn, v = a. That is, a is the volume 
 which the gas eventually takes when pressure increases indef- 
 initely. This may be rationally interpreted by considering a as 
 the absolute volume of the matter within the gas, supposing 
 that the molecules will ultimately touch each other, and not the 
 molecules only but the atoms which make up those molecules. 
 
MEMOIRS ON 
 
 Dupre and M. Hirn have reached a similar conclusion with- 
 in certain limits by different methods, and in a way quite un- 
 like that which I have just explained ; but their inferences 
 would lead to interpretations which are at variance with my re- 
 searches, taken as a whole. 
 
 In fact Dupre, from fundamental formulae in the mechanical 
 theory of heat, which he treats in his work (Dupre, Theorie me- 
 canique de la chaleur), deduces the following law which he calls 
 the law of covolumes, as an approximation of a higher order of 
 accuracy than the law of Mariotte. I will quote it verbatim: 
 
 "At constant temperature the pressures of a mass of gas vary 
 inversely, as the volumes diminished throughout ~by a small con- 
 stant quantity c u . This is to be called the covolume wlien the 
 volume u under normal conditions is the unit of volume." 
 
 For nitrogen, carbon dioxide, and air the covolume of Dupre 
 is positive ; for hydrogen it is negative. Seeking a verification 
 of this law by aid of the numerical data in the classical research 
 of Regnault, Dupre found that this was feasible for hydrogen, 
 as may well be anticipated after what has just been said ; but 
 for nitrogen, and above all for carbon dioxide, the verification 
 leaves much to be desired. It could not be otherwise, since the 
 law of the covolume presupposes that the curve representing 
 the results in the above co-ordinates is straight. This condition 
 is not realized for the case of nitrogen, nor for carbon dioxide, 
 unless it be for temperatures and under pressures for which 
 the covolume becomes precisely contrary in sign to that deduced 
 by Dupre. The law of the covolume with the interpretation 
 given to it by this physicist cannot therefore be admitted. 
 
 M. Hirn has published an elaborate research * on the same sub- 
 ject. Endeavoring to interpret the variations from the law of 
 Mariotte, he points out that even if the molecules of a gas exert 
 no reciprocal action on each other the gas cannot rigorously 
 obey this law, since the variable part of the volume is not the 
 total volume of the gas, but rather the latter diminished by the 
 volume of the atoms. This is equivalent to admitting the quan- 
 tity a defined above. M. Hirn contends that it is merely the 
 variable part of the volume which ought to enter into the ex- 
 . pression of Mariotte's law, a conclusion far from evident. 
 
 For the case in which one may not neglect the interactions 
 
 * Hirn : Theorie mecanique de la clialeur, t. ii. 
 40 
 
THE LAWS OF GASES 
 
 of the molecules, M. Him introduces an internal pressure to 
 be added algebraically to the external pressure, and the general 
 expression of the law for constant temperature becomes 
 
 p and p being the internal pressures corresponding to the vol- 
 umes Fand V. For hydrogen p and p' would be approxi- 
 mately zero, whence 
 
 P ( V a) = const., 
 
 an expression which M. Him verifies by aid of the data of 
 Regnault. 
 
 For nitrogen this correction of volume becomes insufficient, 
 and does not even retain the same sign. It is therefore neces- 
 sary, in order to explain the variation of this gas, to admit an 
 internal pressure of marked value. Now if this is the case 
 with nitrogen for pressures less than 20 atmospheres, one cannot 
 assuredly deny that it must also be the case for hydrogen when 
 this gas is reduced to the three-hundredth part of its volume. 
 But for pressures as large as 430 atmospheres, and very cer- 
 tainly even for higher pressures, the law for the compressibility 
 of hydrogen is given by the equation 
 
 p ( V a) =const. 
 
 as rigorously as for smaller pressures. The internal pressure 
 is therefore zero. Furthermore, if we examine the data rela- 
 tive to carbon dioxide and ethylene, we again observe that for 
 temperatures near the critical point a large part of the curve 
 becomes straight. This takes place for carbon dioxide at 35 
 from 100 to 430 atmospheres ; and the same phenomenon is 
 observed at 18 C. between the same limits of pressure, even 
 though the body is now a liquid i.e., has been subjected to 
 what is properly termed liquefaction. Under these conditions 
 the compressibility of the gas is thus represented by the relation 
 
 p( V a )= const., 
 
 and a has the same value as at 100 C., and higher temperatures 
 where the same formula represents the phenomenon from the 
 lowest pressures upward. Hence one may argue that under 
 circumstances in which the internal pressure ought to attain a 
 very large value (at 35 between 100 and 400 atmospheres), this 
 pressure would actually vanish from the equation; whereas it 
 would show a preponderating influence between normal press- 
 ure and 100 atmospheres, where it ought itself to explain the 
 greater part of the variation of volume. 
 
 * 41 
 
MEMOIRS ON 
 
 I have already shown that, even after making full allowance 
 for the atomic volume, the occurrence of an internal pressure 
 in such a way as to represent a mere addition to the external 
 pressure is quite insufficient to give an account of the variations 
 from Mariotte's law. The demonstration was on that occasion 
 based on numerical difference's of rather small value. To-day, 
 with the new results which I have reached, I am able to make 
 this fact much more evident. I will therefore take up the 
 demonstration again and complete it, introducing in its turn 
 the atomic volume. 
 
 Let V be the volume of the gas at the pressure P and the 
 
 temperature T\ let a be the corresponding atomic volume; 
 
 let the gas be compressed as far as pressure P', and let V be 
 
 the new volume at the same temperature. Hence one obtains 
 
 (P+p)(V-a) ! 
 
 lP'+p')(V'~a) (1) 
 
 p and p' being the internal pressures for the volumes Fand V. 
 
 Now let the gas be heated as far as T' degrees and let P l be 
 the pressure needed to keep the volume at V. The internal 
 pressure, if it depends only on the mean distance apart of the 
 molecules, will again be p. 
 
 Compress the gas until its volume has diminished to V and 
 let PI be the pressure needed for this purpose. The internal 
 pressure will again be p' for the reason specified. Hence we 
 should obtain : {Pj + p)(r _ a ) 
 
 (/Y+/)(F'-a)- 
 Equations (1) and (2) may be put under the following form : 
 
 P(V-a) p'(V'-a) -J(F-q). 
 
 'p'(V'-a)~ P'(V'-a) 
 
 (& ZiLEz^) - 1 ,/'(F'-a) -p(F-a) 
 
 '- ' 
 
 Put p'(V'-a)-p(V-a) () 
 
 P'(V'-a) 
 
 nd y(F'-a)-XF-) 
 
 Pi(V'-a) 
 
 rp 
 
 The relations (3) and (4) now become : 
 P'(F'~) =1+ ^ 
 
 P'(V~-a) =l + a '' 
 
 42 
 
/< 
 
 ( Tl . 
 
 THE LAWS OF GASES 
 
 Here a and a' are the variations from Mariotte's law, after 
 the correction for atomic volume has been applied ; in other 
 words, the discrepancy of the law : 
 
 p ( V a) = const. 
 
 Furthermore, by dividing (5) by (6) : 
 
 ' 
 
 Hence the departure from the law P(V a) = const. must be 
 in the inverse ratio of the corresponding final pressures P t 
 and P,'. 
 
 As an example, data may be given for carbon dioxide at 35. 4 
 between the pressure limits 30 and 70 atmospheres. From the 
 isotherms one finds at once that at pressures of 40 and 220 at- 
 mospheres at 100 the gas has the same volume as at 30 and 70 
 atmospheres at 35. 
 
 Hence a _220 
 
 ^"lo"' 
 
 The volumes V and V are given in turn by the ordinates 
 corresponding to 30 and 70 meters of mercury. It suffices to 
 divide these by the corresponding pressures. The value of a 
 is deduced from the straight part of the curves of which it is 
 the angular coefficient. Thus without difficulty 
 
 F=7.9, F' = 1.03, a = 0.625. 
 Hence one should have 
 
 (7.9-. 625) 30 
 
 (1.03-.625) 70~~ 
 
 (7.9-. 625) 40 
 
 = 1 + a , 
 
 (1.03-.625)220 
 whence, after reduction, 
 
 a 5.65, 
 a'=1.81. 
 Finally, in accordance with equation (7), 
 
 5.65 220 
 
 1^=40- or 3.12 = o.o, 
 
 an absurdity out of all proportion with such discrepancies as 
 might arise out of mere errors of experiment, even when the 
 approximate method of verification is taken into account. 
 
 The so-called internal pressure cannot therefore be admitted 
 into gaseous kinetics in so far as this pressure is to depend only 
 on the mean distance apart of the molecules i.e., to be a 
 
 43 
 
MEMOIRS ON 
 
 function of volume only. It is also a function of temperature, 
 as M. Blaserna* has already inferred elsewhere. 
 
 In his calculations of the internal work of a gas M. Him 
 makes frequent use of internal pressure. The results at which 
 he thus arrives may therefore appear discordant with my own 
 results. Without wishing to enter into a detailed discus- 
 sion, I will remark that this disagreement can onJy be appar- 
 ent ; it is due simply to the fact that rather in the interior of 
 the molecule than between integrant molecules is the larger 
 part of the internal work expended. It does not follow that 
 the values of internal work numerically calculated are errone- 
 ous. 
 
 M. Clausius has evolved a theory which has since become 
 classic, and which can very easily give an account of the dis- 
 crepancies of Mariotte's law. This theory, which in its incep- 
 tion is traceable to Bernoulli, and the first kinetic explana- 
 tion of Mariotte's law to Kronig, interprets pressure as due to 
 the impact of the molecules of a gas on the walls of the vessel 
 holding it. Pressure thus depends on the kinetic energy of 
 the translational motion. 
 
 When a gas is compressed at constant temperature, it suffices 
 to assume that a part of the translational or intermolecular 
 energy is transformed into intramolecular energy or into the 
 energy of molecular rotation, to give a complete account of 
 the discrepancy of Mariotte's law. For the result would be a 
 diminution of pv. As the effect of atomic volume would 
 make the law deviate in a contrary sense, one is led to antici- 
 pate the differing phases through which the compressibility of 
 a gas passes, according as one or the other of the two causes 
 supervenes. It is even possible that both causes may annul one 
 another, and that the gas thus accidentally obeys Mariotte's 
 law, as is the case, for instance, in the region of minimum 
 ordinates. 
 
 Taken as a whole, the results which I have reached show 
 pretty clearly that a special theory for gases and another for 
 liquids is out of the question. Consider, for example, the 
 isotherms of hydrogen : how is it possible to admit one theory 
 to explain the facts represented by one part of the curves and 
 another theory to explain the rest, seeing that their form shows 
 
 * Blaserna : Comptes rendus, t. Ixix., 1869. 
 44 
 
THE LAWS OF GASES 
 
 
 
 conclusively that a phenomenon of perfect continuity has been 
 observed ? Now the theory of impact cannot be applied to 
 hydrogen under 400 atmospheres, since under these conditions 
 the proximity of its molecules would make it rather a liquid 
 than a gas. As long as questions on the condition of carbon 
 dioxide or of ethylene at ordinary temperatures are upper- 
 most, one may infer that the two parts of an isotherm situated on 
 each side of the minimum ordinate are subject to the different 
 laws ; inasmuch as an abrupt variation, which may reasonably 
 be interpreted as limiting two different thermal states, sepa- 
 rates them. But this is no longer applicable when the gases 
 are subjected to higher temperatures, nor for hydrogen (as I 
 have stated) even at ordinary temperatures. 
 
 It is very remarkable that the law given by the equation 
 p(V a) = const., which has been the immediate outcome of 
 my experiments, and which appears to be the limiting law tow- 
 ards which all gases converge when their temperatures are 
 raised, is the same law which is in action in the neighborhood 
 of the critical point, whenever the compressibility of a body is 
 considered throughout increasing pressures. Thus it is rather 
 a law for the liquid than for the gaseous state. I will even add 
 that it is specifically the law of liquids at least, within the 
 limits of actual experimental inquiry; for it appears from the 
 group of isothermals that carbon dioxide at 18, which is 
 then truly liquid, follows exactly the same law. Its curve is 
 a straight line whose angular coefficient is a. Thus we arrive 
 at a result which appears at first sight quite paradoxical, that 
 elevation of temperature transforms the gas into the state of 
 a perfect liquid; and that the region of branches of the iso- 
 therms situated on the left of the line of minimum ordinates, 
 the region which corresponds accurately to the gaseous state 
 in the ordinary sense of the word, is a period of turbulence 
 terminating in the phenomenon of liquefaction properly so 
 called. This phenomenon disappears when temperature rises 
 indefinitely and the body becomes a perfect fluid, to employ a 
 word which is at once applicable both to the liquid and the 
 gaseous states. 
 
 The state in question is defined by the simple equation 
 p ( V a) = const., or pW const., if W is the interatomic vol- 
 ume. The law thus expressed is so very simple that one is 
 naturally induced to seek an explanation for it depending sim- 
 
 45 
 
MEMOIRS ON 
 
 ply on a consideration of interatomic volume ; for what I have 
 already said about internal pressure shows, among other things, 
 that internal pressure does not appear to exert as much in- 
 fluence on the changes of volume of a gas or of a liquid as has 
 been usually supposed. This influence should be reducible to 
 disturbances quite of secondary importance in their bearing 
 on the law in question disturbances which may, for example, 
 be of the order of magnitude of the discrepancies of Mariotte's 
 law occurring within the limits of pressure explored by Reg- 
 nault. 
 
 To reach an explanation based purely on the consideration 
 of atomic volume, let us observe in the first place that the law 
 PTF=const. is capable of the following enunciation : The be- 
 havior of the body during compression is such as if an infinite- 
 ly subtle fluid rigorously subject to the law of Mariotte per- 
 vaded the whole space between the molecules, the material 
 particles or the groups which they form showing only a negli- 
 gible amount of translational kinetic energy and producing an 
 effect only by their presence i.e., by the volume which they 
 delimit i-n the same way as if they were ordinary walls of the 
 region. 
 
 Why may not this fluid be the ether in a certain degree of 
 concentration ? Such an hypothesis would give a complete 
 account of all observed facts. It by no means excludes the 
 theory of molecular impact, as we have seen ; it merely re- 
 stricts the limits within which kinetic action is applicable. 
 Evidently the ether ought to perform some function relative 
 to the phenomenon with which we have been occupied; but 
 this role has never been specified, nor, so far as I know, has 
 anything been said about it. If one considers the exclusive 
 importance of the ether in optic phenomena, the relation of 
 these to thermal phenomena, and the close connection of the 
 latter with those which we have been investigating, the strong 
 probability that the ether must fulfil some important function 
 is manifest. 
 
 It seems probable that the molecules are surrounded in every 
 thermal state solid, liquid, or gaseous with atmospheres of 
 ether. These atmospheres account for their perfect elasticity, 
 as evidenced in the kinetic theory of gases an elasticity which 
 it would be very difficult to explain, or which would be even 
 quite inexplicable, if the molecules were simple i.e., reduced 
 
 46 
 
THE LAWS OF GASES 
 
 to single atoms. Granting this, let a gas be considered at low 
 pressure and at a temperature but little above the critical 
 point. Let the gas be compressed at an initially constant 
 temperature. The theory of molecular impact deduces Ma- 
 riotte's law in the usual way. Changes in the distribution of 
 kinetic energy between the motion of molecular translation, 
 the motion within the molecule, and its rotational motion 
 suffice to explain the discrepancies of the law, to which, in a 
 certain measure, molecular attraction may join its effects. 
 Thus the gas is more compressible than Mariotte's law indi- 
 cates, even if allowance be made for the absolute volume of the 
 atoms. Very soon, however, these with their atmospheres of 
 ether occupy the major part of the volume, and so hamper 
 each other in their movements of translation that the latter 
 virtually vanish. This occurs in the neighborhood of the min- 
 imum ordinate. Finally, for continually increasing pressures 
 the atmospheres of ether will actually become contiguous, and 
 the molecules appear as if suspended therein. The ether now 
 forms a medium which is continuous, and by its reaction pro- 
 duces the observed pressure against the walls of the vessel. If 
 this ether obeys Mariotte's law, which is now to be regarded as 
 the limiting law of an infinitely subtle fluid, the volume which 
 it occupies is exactly W, and PPT^const., or P (V a)=const. 
 Hence, although there has been no liquefaction in the true 
 sense of the word, the body is rather a liquid than a gas, for 
 the reason that the molecular translational motion, which is a 
 criterion for the gaseous state, has vanished. 
 
 With the beginning of an increase of temperature, the ethe- 
 real molecular atmospheres will expand simultaneously with 
 the molecules themselves, and the atoms separate more and 
 more fully until decomposition ensues. Inasmuch as the total 
 volume of the ethereal atmospheres is larger, the law p W= 
 const, ought to begin to apply for a given mass of gas at a 
 larger volume than at the lower initial temperatures. This 
 indeed appears very well to account for the fact that for a 
 given mass of gas the volume corresponding to the minimum 
 ordinate increases with temperature. 
 
 If temperature continually rises, the fraction of the total 
 volume occupied by the ether also continually increases, and 
 when the effect of the latter preponderates the curves will rise 
 and be gradually transformed into straight lines. 
 
 47 
 
MEMOIRS ON 
 
 Perhaps I ought to add, in order to escape an unfavorable 
 issue, that the ether taken into consideration here is that only 
 which is retained by and condensed around the molecules in 
 the form of a molecular atmosphere. The ether which is not 
 so condensed but pervades the molecular spaces, whatever be 
 the distance apart of the molecules, is without relevant in- 
 fluence. This does not oppose any reaction, and for it the 
 walls of the vessel do not exist. 
 
 The hypothesis which I have just formulated thus renders a 
 natural and complete account of the details of the phenomena 
 brought out by experiment. It does not exclude those kinetic 
 theories which have gained general acceptance among physi- 
 cists. So far as I can see, it is not at variance with any estab- 
 lished experimental fact. It restricts the limits within which 
 the theory of impact is apparently applicable by establishing 
 a transition from the liquid to the gaseous state, which may be 
 passed continuously and the mechanism of which is easily in- 
 telligible. Finally, it introduces no difficulty whatever into 
 the phenomenon of liquefaction properly so called. 
 
 I have already stated that the law PW const., which ap- 
 pears to be the general law for fluids, is applicable to liquid 
 carbon dioxide below the critical point, as is evidenced by the 
 straight isotherm for 18 contained in the family of curves. 
 I endeavored to verify the same fact with several liquids, nota- 
 bly w r ith chlorhydric ether, for which I published the compres- 
 sibilities as far as 100 and 37 atmospheres several years ago.* 
 The law was reproduced with a very fair approach to accuracy ; 
 but in order that these verifications may not be over-estimated, it 
 is well to insert the following remark: If the liquid were quite 
 incompressible its isotherm would necessarily be a straight line, 
 for the ordinate would vary proportionally to p, v being con- 
 stant. For liquids in general, therefore, inasmuch as they are 
 nearly incompressible, their curve must differ exceedingly lit- 
 tle from a straight line, no matter what may be the true law of 
 compressibility. It is thus impossible to derive any very cer- 
 tain inferences from the behavior of the greater number of 
 liquids. For liquid carbon dioxide, however, the case is alto- 
 gether different, and, a fortiori, for hydrogen between limits of 
 pressure as far apart as those within which I have operated. 
 
 * Annales de Chimie et de Physique (5), t. xi. ; Memoirs sur la Comprem- 
 bilite des Liquides. 
 
 48 
 
THE LAWS OF GASES 
 
 I have still to give the numerical values of atomic volume, 
 having calculated it for hydrogen, carbon dioxide, and ethy- 
 lene, all of which contain the straight parts of the isotherms 
 clearly defined and of marked extent. In computing the limit- 
 ing directions of the lines for the other gases, one is liable to 
 make a considerable error. 
 
 To obtain a it is adequate to establish the relation 
 
 p(r-.)=p'(r'-a) 
 
 between two pressure values sufficiently far apart and compre- 
 hending a part of the curve sensibly straight. Thus the value 
 of a is deduced from p, p', v, v', given by experiment. Hence 
 one obtains the atomic volume of the mass of gas subjected 
 to the experiments from which the curves were constructed. 
 This mass is defined by the normal pressure and the tempera- 
 ture at which the manometers were charged with gas. 
 
 I have preferred to refer the atomic volume to the unit of 
 volume of the gas at C. and 76 centimetres of mercury, ob- 
 taining the following values : 
 
 Hydrogen 0.00078 
 
 Carbon dioxide 0.00170 
 
 Ethylene 0.00232 
 
 Finally, I may remark that the interpretation given for the 
 value of a is independent of the hypothesis on which the 
 theory of the gaseous state is founded. It will readily be seen 
 that it is enough that the curves of compressibility should 
 tend to become straight lines in the. limit; for under these 
 conditions 
 
 pv = a p + by or Va for jo oo. 
 
 No matter to what theory one may subscribe, therefore, a ap- 
 pears as the smallest absolute volume which the matter can 
 occupy. One naturally infers that this is the atomic volume. 
 This remark is particularly applicable to hydrogen, the iso- 
 therms of which are practically straight throughout their 
 whole extent. For the other gases the determination of a rests 
 on the inferences deduced from the curves as a whole, but less 
 certainly. The results are therefore given with less assurance. 
 
 To pursue this subject exhaustively within the limits which 
 I have set for myself, it will still be necessary to study the 
 compressibility under conditions of pressure lower than those 
 
MEMOIRS ON THE LAWS OF GASES 
 
 occurring in the present research. These experiments will be 
 made directly with an open manometer. I hope to carry the 
 measurements as far upward as 300. I hope also to trace the 
 phenomena further into the region of extremely low pressures 
 a few millimetres, for instance on which subject 1 have al- 
 ready published* an introductory paper. 
 
 Returning again to these experiments,, I shall be in a position 
 to add many material improvements to the method which I 
 formerly employed, and above all to the apparatus. They will 
 be completed, I hope, in the course of the next academic year. 
 
 * Annales de Ghimie et de Physique, t. viii., 1876 
 
MEMOIR ON THE ELASTICITY AND 
 
 THEEMAL EXPANSION OF FLUIDS 
 
 THROUGHOUT AN INTERVAL 
 
 TERMINATING IN VERY 
 
 HIGH PRESSURES 
 
 BY 
 
 E. H. AMAGAT 
 
 (Anncdes de Chimie et de Physique, 6 Serie, t. xxix., 
 
CONTENTS 
 
 PAGE 
 
 PART L Method* of Manipulation : 
 
 Introduction 53 
 
 Methods of Experimentation : 
 
 1. The Measurement of High Pressures Manometre d Pis- 
 
 tons Libre 55 
 
 2. Apparatus for Extremely High Pressures : 
 
 Method of Electrical Contact 61 
 
 Details of Manipulation 65 
 
 Plan of a Series of Measurements 67 
 
 3. Apparatus for Higher Temperatures : 
 
 Method of Sights 71 
 
 Preliminary Operations 75 
 
 PART II Data for Oases. 77 
 
 Results Obtained by tJie First Method (Method of Electrical 
 
 Contacts] 78 
 
 Results Obtained by the Second Method (Method of Sights) . . 80 
 Examination of the Results : 
 
 General Laws 89 
 
 Coefficients of Expansion at Constant Pressure (- j . . 94 
 
 Variation of the Coefficient of Expansion with Press- 
 ure , 97 
 
 Variation of the Coefficient of Expansion with Tem- 
 perature 98 
 
 Coefficients of Expansion at Constant Volume fi=(- Y 
 
 and Pressure Coefficients B = 101 
 
 Variation of the Coefficients B and (3 with Volume 104 
 
 Variation of the Coefficients B and fi with Temperature. 104 
 
MEMOIR ON THE ELASTICITY AND 
 
 THERMAL EXPANSION OF FLUIDS 
 
 THROUGHOUT AN INTERVAL 
 
 TERMINATING IN VERY 
 
 HIGH PRESSURES 
 
 BY 
 
 E. H. AMAGAT 
 
 PART I. METHODS OF MANIPULATION 
 INTRODUCTION 
 
 IN the Memoir which I publish to-day I have brought to- 
 gether the whole of my researches on the expansion and com- 
 pressibility of fluids,* in so far as they have occupied me dur- 
 ing the last ten years. A part only of the results has been 
 published in the Comptes Rendus de V Academic des Sciences; 
 the experimental portions, moreover, were sketched with the 
 utmost brevity compatible with clearness. 
 
 The present researches for gases are a direct continuation of 
 my earlier work on the same subject. In the latter the limits 
 of pressure and of temperature employed were too narrow, and 
 the number of isotherms mapped out not great enough to re- 
 veal certain relations which appear very clearly in the present 
 results. Such are, for example, the form of the isotherms in 
 the region of the critical point which lay beyond the limits of 
 my first group of curves ; furthermore, the contours of these 
 
 * The parts of this great memoir referring to liquids will not be in- 
 cluded in the present translation. 
 
 53 
 
MEMOIRS ON 
 
 curves in the region lying to the right of the locus of minimum 
 ordinates, and in which the isotherms under very great press- 
 ure seem to merge into straight lines, etc. 
 
 As for liquids, the question was virtually untouched when 
 these researches were begun. The increase of the coefficient 
 of compressibility with temperature had been observed for 
 some liquids, together with the contrary effect for water. I 
 myself extended these results, in a memoir published in 1877, 
 to a large number of liquids, and within limits of pressure and 
 of temperature beyond any which had been applied at that time ; 
 but the laws as a whole were yet to be investigated, the deter- 
 mination of pressure coefficients was not even attempted, the 
 data relative to the variation of the coefficient of compressibil- 
 ity with pressure were altogether contradictory. Well-known 
 treatises of physics even to-day contain errors in relation to 
 this subject which surpass the limits of plausibility. Since 
 that time, however, several important researches bearing on 
 these phenomena have been published outside of France. 
 
 The researches which I am about to describe have been made 
 with a view towards reaching the highest attainable pressures, 
 both for liquids and for gases. It is my purpose, furthermore, 
 to make special investigations for the low pressures i.e., for 
 the first one hundred or two hundred atmospheres, and there- 
 after to co-ordinate them in such a manner as to give a com- 
 plete presentation of the phenomena. Experiments devised 
 to reach a thousand or several thousand atmospheres must at 
 lower pressures of necessity show an inferior degree of accuracy 
 than may be reached in experiments specially adapted to the 
 latter. Circumstances have not permitted me to terminate 
 this research, but the most difficult part of it is finished. 
 
 In this place I may be permitted to say that the instruments 
 which are to be described, as well as all others used in my re- 
 searches for upwards of fourteen years (1877 to 1891), were con- 
 structed, in the workshop attached to my department (service) 
 at Lyons, by M. Gianotti (at present instrument -maker in 
 Lyons). My tasks have, throughout, been singularly facili- 
 tated both by his skill in construction and by the earnestness 
 with which he aided me in the experimental work. 
 
 Glass apparatus was made by M. Alvergniat, or by his suc- 
 cessor, M. Chabaud. Indeed, all the apparatus, either of ordi- 
 nary or of cut glass, which has been used in my experiments 
 
 54 
 
THE LAWS OF GASES 
 
 for twenty-five years or more, was constructed by these gentle- 
 men. I need not further advert to their services, cheerfully 
 rendered in the cause of science. 
 
 I shall first describe the methods and the apparatus. They 
 are of like construction, both for liquids and for gases, except 
 as to the piezometer containing the fluid and the manner of 
 charging it. I shall begin with the apparatus for pressure 
 measurement. 
 
 METHODS OF EXPERIMENTATION 
 
 The Measurement of High Pressures " Manometre a Pistons 
 
 Litres." 
 
 When I undertook the present researches there was no in- 
 strument available for the accurate measurement of pressure 
 beyond the range within which it was customary to compare 
 the well-known empiric pressure-gauges with the open ma- 
 nometers. In practice closed gas manometers are subject to 
 serious inconveniences. Moreover, they cannot be employed 
 above 420 atmospheres, this being the upper limit of the meas- 
 urements which I made, in 1878, with an open manometer in 
 the shaft of the mine at Verpilleux. 
 
 The principle of the instrument improperly called manometre 
 de Desgoffe* solves the question theoretically; but the practical 
 construction adopted was actually so defective that no reliance 
 could be put on its indications. The manometers of the valve 
 or plug type may perhaps render service in certain cases. M. 
 Marcel Deprez has improved them by replacing for the first 
 time, I believe the valve by a free plunger (piston litre), which 
 does not allow water to pass except with extreme slowness. 
 But these instruments even when perfected are not available in 
 researches which cannot well be conducted without a pressure- 
 gauge of continuous registry. 
 
 The grave difficulty in the way of a realization of Gaily - 
 Cazalat's idea is this : to make the pistons perfectly free to 
 move while at the same time obviating leakage. For the large 
 piston the difficulty is in a certain measure solved by the ad- 
 
 * This instrument was invented by Gally-Cazalat ; constructed at first 
 by Clair, then by Bianchi, and finally by Desgoffe. 
 
 55 y v- OF THB 
 
 UNIVERSITY 
 
MEMOIRS ON 
 
 dition of au india-rubber membrane. Nevertheless, this in- 
 genious device is not quite beyond criticism ; for in the first 
 place the sectional surface is badly determinate, while in the 
 second the action of the membrane gives rise to an error which 
 the operator must either endeavor to estimate or to obviate. 
 In the first instruments which I constructed I retained the 
 membrane design, but an index rigidly attached to the large 
 piston enabled me to follow its motion, and, therefore, that of 
 the membrane also. It was then my purpose to provide the 
 apparatus with a regulating pump, which by injecting a vari- 
 able quantity of liquid below the membrane would enable me 
 to keep it always in the same horizontal plane, thus suppress- 
 ing nearly completely the action referred to. Later I found it 
 more advantageous to do away with the membrane altogether 
 and to leave the large piston entirely free. 
 
 To secure freedom from leakage, I found it sufficient to give 
 the piston a suitable thickness and to replace the actuating 
 water by a lubricating and at the same time slightly viscous 
 liquid ; castor-oil is very serviceable for this purpose. 
 
 The analogous difficulty remained for the case of the small 
 piston, which, experiencing strong pressure in a leather-lined 
 stuffing-box, moved only with difficulty and by jerks. It was 
 necessary to make this piston free, like the first, but the con- 
 dition of no leakage was here very much more difficult of at- 
 tainment in spite of the small section. For while the large 
 piston receives only the relatively small pressure of the counter- 
 poising column of mercury, the enormous total pressure which 
 is to be measured bears down upon the small piston. I suc- 
 ceeded, however, in meeting the present difficulty by the identi- 
 cal artifice i.e., by using a sufficiently viscous liquid, in this 
 case molasses. Nevertheless, the function of this body is some- 
 what different from that of the castor-oil : for while the oil con- 
 tinually lubricates parts, oozing with extreme slowness between 
 them in a way not to interfere with effective action, the mo- 
 lasses penetrates the space around the piston supposed to be 
 well oiled in advance with very great difficulty even at very high 
 pressures. When the molasses has succeeded in penetrating 
 and removing the oil, the apparatus still functions, although 
 with loss of same of its original sensitiveness. It is then pref- 
 erable to detach the small piston and to clean it. When the 
 apparatus has been Adjusted with care, it is sufficient to place 
 
 56 
 
THE LAWS OF GASES 
 
 an object of even insignificant weight on the large piston to 
 produce a corresponding small ascent of the column of mer- 
 cury. The small piston is in general less sensitive, above all 
 after the molasses has penetrated between it and the socket. 
 Finally I succeeded in quite annulling the resistance due to 
 friction by impressing on both pistons a slight movement of 
 rotation. An analogous artifice has long been employed by 
 
 FIG. 1. FREE-PISTON MANOMETER (Manometre d Pistons Libres). 
 
 M. Bourdon to overcome the friction of the piston of the ap- 
 paratus used in standardizing his spirals ; but while the leather- 
 lined stuffing-box requires a rapid movement of rotation in 
 order to obviate the friction of a tight fit, my apparatus needs 
 only a slow and slight angular displacement of the pistons in 
 order that the column of mercury may at once take its definite 
 position of equilibrium. 
 
 Fig. 1 gives a section of the apparatus. The liquid trans- 
 mitting pressure arrives by the tube, c, through a channel in the 
 
 57 
 
MEMOIRS ON 
 
 piece of steel, b, screwed to the brass * lid, a. This piece secures 
 the socket of tempered steel, d, holding it down free from leak- 
 age by aid of round leather washers. The small piston, also 
 of tempered steel, moves up and down in this socket. The 
 parts are so fashioned that a small chamber, 00, is left below 
 b. Into this the charge of molasses is to be put. The lower 
 end of the small piston abuts against a small plane of tempered 
 steel, which is seen in the figure, screwed to the centre of the 
 large piston, P. A valve-screw, d' , may be raised to admit of 
 the escape of air from below in adjusting the apparatus. Cir- 
 cular grooves are cut equatorially around the outer walls of the 
 large piston. The oil accumulates in these channels during 
 its upward leakage, and finally reaches the hollow part or cup 
 of the large piston. The latter moves up and down in a mas- 
 sive envelope, also of brass. This is screwed down to a heavy 
 trough of cast-iron, serving as the base of the apparatus, by a 
 crown of square-headed bolts, and further secured to the lid, a, 
 of the apparatus by a second crown of longer bolts. A key, 
 not shown in the figure, may be attached to the large piston at 
 its centre, for the purpose of withdrawing or of inserting it. 
 In such a case the key replaces the small plane of steel. 
 
 On the right side of the figure, and screwed to a lateral pro- 
 jection of the trough, is the steel coupling carrying the glass 
 tube in which the mercury column rises. This coupling con- 
 sists of two parts : the lower part carries a stopcock, and thus 
 the operator is able to remove the glass tube, even when the 
 trough is charged, without spilling the mercury within it. At 
 the left of the figure, and symmetrically placed, is the regu- 
 lating pump, and this, for a reason similar to the one just given, 
 also consists of separable parts with a stopcock in the lower. 
 The channel by which the oil, H, is injected is prolonged by a 
 tubulure extending upward much above the mercury surface, 
 Jf, in order that this may under no condition reach the pump, 
 which is of brass, and thus in danger of amalgamation. 
 
 The angular movement of the two pistons is produced by the 
 steel rod, mm', screwed f to the prolongation of the small pis- 
 
 * In the case of instruments for measuring very high pressures, the 
 strength of the brass bolt crown is insufficient ; the central part of the lid, 
 as shown by the dotted lines, should be made of steel. 
 
 f For pistons of very small diameter, this prolongation is enlarged and 
 different in form. 
 
 58 
 
THE LAWS OF GASES 
 
 ton. This rod passes between two pins, i, screwed to the mar- 
 gin of the large piston, arid leaves the apparatus through a win- 
 dow in the upper part of the cylinder. Thus both pistons may 
 be put into the same horizontal angular motion, which is trans- 
 mitted by a simple arrangement not shown in the figure. The 
 regulating pump makes it possible to keep the stem, mm', at a 
 height such as will not interfere with the upper or lower edge 
 of the window. Moreover, by an inverted action of the appur- 
 tenances of the manometer, the pump maybe made to produce 
 very considerable pressures above the small piston and in the 
 space where the bodies subjected to experiment are placed ; it 
 is often convenient to make use of this method to regulate the 
 pressure at the moment of measurement. M. Vieille * has re- 
 cently made a very happy application of this artifice, in con- 
 nection with his studies on the behavior of the crushing ma- 
 nometer (manometre-crusliers). 
 
 If well constructed, my apparatus will give pressure -values 
 of remarkable uniformity, the accuracy of which depends only 
 on the sectional ratio of the two pistons. The sensitiveness 
 can be increased at pleasure by increasing the value of this 
 ratio and making use of a graded series of pistons. The ap- 
 paratus which I used was provided with two large pistons, the 
 one 6 centimetres and the other about 12 centimetres in di- 
 ameter, together with a series of small pistons, the smallest 
 being 5.527 millimetres in diameter. 
 
 The absolute error is about the same throughout the whole 
 scale of pressures. The relative error would become intoler- 
 ably large if a few atmospheres only were to be measured, 
 which, however, is beyond the purposes of the instrument. It 
 is, nevertheless, my intention to construct a small model special- 
 ly designed for the lower order of pressures, and I hope to find 
 it relatively quite as reliable. 
 
 On several occasions I made comparisons of data for the 
 same pressures furnished simultaneously by two different free- 
 piston manometers, or when one of these was replaced by a 
 closed gas manometer. The agreement of the former was al- 
 ways very satisfactory, but this was usually less so with the gas 
 manometers. I do not hesitate to ascribe these discrepancies 
 to the difficulty of manipulating the latter. Here is the com- 
 
 * Memorial des Poudres et Salpetres, v. 
 
MEMOIRS ON 
 
 parison of the free-piston manometer which I constructed in 
 1885 for M. Tait, with two nitrogen manometers and an air 
 manometer. Pressures are given in atmospheres. 
 
 TABLE 1. MANOMETERS 
 
 NITROGEN 
 
 PISTON 
 
 NITROGEN 
 
 PISTON 
 
 AIR 
 
 PISTON 
 
 226 Aim. 
 
 224: At m. 
 
 102 Atm. 
 
 103 Atm. 
 
 217 Atm. 
 
 215 Atm. 
 
 278 " 
 
 275 " 
 
 154 " 
 
 154 " 
 
 262 " 
 
 263 " 
 
 328 " 
 
 326 " 
 
 213 " 
 
 215 " 
 
 305 " 
 
 306 " 
 
 391 " 
 
 387 " 
 
 256 " 
 
 257 " 
 
 358 " 
 
 362 " 
 
 438 <{ 
 
 438 " 
 
 299 " 
 
 297 " 
 
 401 " 
 
 406 " 
 
 
 
 363 " 
 
 359 " 
 
 
 
 
 
 408 " 
 
 402 " 
 
 
 
 Never did the comparisons of free-piston manometers present 
 like divergencies. 
 
 The following table contains a comparison between the re- 
 sults given by a membrane manometer with but one free piston 
 and a manometer with two free pistons : 
 
 TABLE 2. MANOMETERS. 
 MEMBRANE. TWO PISTONS. RATIO. 
 
 103 Atm.. , 102 Atm. . . 1.010 
 
 156 
 215 
 
 260 
 304 
 368 
 444 
 550 
 604 
 697 
 
 154 
 213 
 
 257 
 301 
 364 
 439 
 545 
 600 
 692 
 
 1.013 
 1.010 
 1.012 
 1.010 
 1.011 
 1.011 
 1.009 
 1.007 
 1.007 
 
 The agreement of piston and gas manometers improves when 
 the latter are used under the best conditions. 
 
 In Table 3 are the results of a comparison with an air and a 
 nitrogen manometer, devised for very high pressures, much 
 more sensitive than the above, and directly graduated for each 
 gas by comparison with a column of mercury in one of the 
 
THE LAWS OF GASES 
 
 towers of the Fourviere cathedral in Lyons that is, under the 
 best conditions possible. The free-piston manometer was it- 
 self so adjusted that fractions of an atmosphere were easily read 
 off. 
 
 TABLE 3. MANOMETERS 
 
 AIR 
 
 PISTONS 
 
 NITROGEN 
 
 PISTONS 
 
 OPEN 
 MANOMETER 
 
 PISTONS 
 
 20.36 Atm. 
 
 26.32 Atm. 
 
 26.29 Atm. 
 
 26.50 Atm. 
 
 1.66 Atm. 
 
 1.74 Atm. 
 
 32,39 " 
 
 32.34 " 
 
 32,51 " 
 
 33.59 " 
 
 2.95 " 
 
 3.02 " 
 
 38.34 " 
 
 38.44 " 
 
 39.12 ' 
 
 39.21 " 
 
 5.07 " 
 
 5.16 " 
 
 44.98 " 
 
 45.00 " 
 
 45.77 ' 
 
 45.81 " 
 
 6.52 " 
 
 6.61 " 
 
 50.92 " 
 
 51.05 " 
 
 52.26 ' 
 
 52.41 " 
 
 
 
 57.37 " 
 
 57.50 " 
 
 58.12 ' 
 
 58.87 " 
 
 
 
 64.24 " 
 
 64.16- " 
 
 65.35 < 
 
 65.53 " 
 
 
 
 72,15 " 
 
 72,45 " 
 
 71.00 " 
 
 71.36 " 
 
 
 
 Finally, in the last two columns, the table contains a com- 
 parison, throughout a few atmospheres only, with an open 
 mercury manometer, the errors of which may be regarded 
 practically zero. The discrepancy is obviously inadmissible for 
 pressures as small as these ; but for higher pressures, 50 or 
 60 atmospheres for example, the absolute error not becoming 
 larger, the results are exceedingly satisfactory. 
 
 For the series of measurements reading upward as far as 
 3000 atmospheres, I chose a pair of pistons such that one at- 
 mosphere was equivalent to 1.601 millimetres of mercury at 
 C. For the series limited by 1000 atmospheres, the equiva- 
 lent height was 4.99 millimetres. In each case I selected those 
 sectional ratios which gave me the highest attainable sensitive- 
 ness for the case of a column of mercury 5.20 metres in height, 
 the maximum elevation at my disposal. 
 
 2. APPARATUS FOR EXTREMELY HIGH PRESSURES 
 
 Method of Electrical Contact. 
 
 The methods of which I made use in my preceding re- 
 searches do not admit of being carried much above 400 atmos- 
 pheres. It is very difficult to obtain glass tubes which will 
 resist interior pressures more intense than this. To solve 
 this difficulty by plunging the piezometer bodily into a stronger 
 
 61 
 
MEMOIRS ON 
 
 cylinder, necessarily metallic and opaque, presents grave diffi- 
 culties in regard to the reading of volumes. Otherwise it is 
 the method of Oersted. The difficulty in question was first 
 avoided by means of gravitational apparatus, or by covering the 
 interior of the stem of the piezometer by a film which is dis- 
 solved by the liquid transmitting the pressure, thus indicating 
 the height to which it has been raised. These procedures have 
 two serious defects : aside from the fact that they merely give 
 the maximum of the height to which the liquid has been raised, 
 they are quite impracticable for the construction of a regu- 
 lar series. They have given rise to very grave errors. The 
 method pursued for gases by Natterer, which consisted in com- 
 pressing a known volume of gas into a given space, repeating 
 the operation a great number of times and determining the 
 pressure corresponding to each accession, is certain to be sur- 
 rounded with great difficulties, and rapidly becomes quite im- 
 practicable if one endeavors to raise the temperature. The 
 work of Natterer is none the less extremely remarkable, par- 
 ticularly if the time when it was done (1851) is called to mind. 
 It is hard to explain why it has remained so long unknown in 
 France. 
 
 At the time when I began these researches that is, about 
 1882 M. Tait was engaged with a study of the compressibility 
 of water, and he called my attention to the method of electric 
 contacts which he employed in his researches. Among other 
 things, I had also thought of this artifice, but I had as yet 
 made no trial of it. Upon the recommendation of the eminent 
 physicist I tried it at once ; and since then I have employed no 
 other method, either for liquids or for gases, in all series of 
 measurements carried to the highest attainable pressures and 
 at temperatures not exceeding 50. 
 
 Fig. 2 gives a sectional elevation of the apparatus construct- 
 ed for these researches. The receiver, or barrel, GG, in which 
 the piezometer is placed is a cylinder of steel 3 centimetres 
 in diameter internally, and surrounded by a steel jacket, G'G', 
 to a point about as far down as the bottom of the aperture 
 within. The total outer diameter is 18 centimetres, the avail- 
 able depth of the receptacle below the position of the upper 
 junction is about 88 centimetres. The somewhat excessive pro- 
 longation of the unjacketed breech has a special purpose to 
 which I shall refer below. Pressure is transmitted by a charge 
 
THE LAWS O 
 
 ES 
 
 of water injected by a force-pump, and enters at D by way of 
 the valve-coupling, i?, screwed to the upper part of .^fcne receiver 
 on the right. When the pressure attains a certain value de- 
 
 FIG. 3. 
 
 \ J 
 
 FIG. 2. 
 
 FIG. 2. PRESSURE APPARATUS WITH ELECTRICAL CONTACTS. 
 FIG. 3. PIEZOMETER FOR GASES. 
 FIG. 4. PIEZOMETER FOR LIQUIDS. 
 63 
 
 FIG. 4. 
 
MEMOIRS ON 
 
 pending on the upper limit which is to be reached, the screw- 
 valve is closed, and compression is thereafter continued with 
 the use of the device screwed to the head of the receiver. The 
 central piece, A, is pierced by an aperture 16 millimetres in 
 diameter, in which a cap-shaped leather washer, C (drawn in 
 larger scale at the side), moves up arid down. This washer has 
 the form of a little cylinder with a flat base. It is pushed for- 
 ward by a rod of steel, P, advancing with slight friction and 
 terminating in a cone at its upper end. Here the motion is 
 impressed upon it by a steel screw, F, the threads of which are 
 2 millimetres apart and move in a nut of brass carried by a 
 second hollow cylinder of steel, B, surrounding the central 
 piece, A. This second cylinder is screwed to the jacketed re- 
 ceiver, against which it presses the central piece, A, making a 
 pressure-tight joint with it by the aid of a leather washer. 
 The screw is actuated by a four -armed lever seen at the 
 top of the apparatus. At the left, on the same level with the 
 influx valve, there is a special attachment, F, of steel, adapted 
 to carry the electric current into the piezometer, insulated from 
 the body of the apparatus. This is attained by aid of a small 
 cone of steel, K, preliminarily inserted into the channel within 
 the piece, F, and which is wedged after having been surround- 
 ed by a very thin, small conical shell of ivory, 00, insulating 
 perfectly. Moreover, the taper of the cone is so directed that 
 the internal pressure will force it into more intimate contact 
 with its surroundings. The small steel cone joins the ends of 
 the conducting wires, which are screwed into it in the manner 
 detailed in the enlarged figure. This attachment has never 
 shown the least trace of leakage. 
 
 On a level with the influx valve and the attachment, F, there 
 is still a third coupling, not shown in the figure, which puts the 
 barrel in connection with the manometer (these three pieces 
 are in reality placed so as to divide the circumference of the 
 cylinder into three equal parts). The connecting tube is about 
 2 meters long and made up of three parts bored at the lathe, 
 the last piece being afterwards bent down by forging. I at first 
 employed thick tubes of drawn steel, but they burst at about 
 2000 atmospheres. 
 
 The piezometer containing the fluid to be compressed is of a 
 form shown separately in Fig. 3 for gases and in Fig. 4 for liq- 
 uids. The stern carries a series of fine platinum wires laterally 
 
 64 
 
THE LAWS OF GASES 
 
 inserted into the glass and reaching as far as the middle of 
 the bore. Between each thread there is inserted an electric 
 resistance wrapped around the tube. These resistances are 
 made up of wire covered with india-rubber, and a small part of 
 each coil is exposed so as to be soldered to the corresponding- 
 ends of the platinum wires. The whole is then covered by a 
 wrapper, insulating perfectly even when plunged in mercury, 
 and remaining sufficiently soft to insure an equal compression 
 of the glass on opposite faces. When the piezometer is placed 
 within the barrel, the upper terminal is joined to the prolonga- 
 tion seen within the cone of the attachment, F, contact being 
 thus completed throughout. When the mercury into which 
 the lower end of the piezometer is plunged rises in the tube 
 conformably with the increasing pressure, and just touches the 
 first of the lateral platinum wires, the current may be closed 
 between any part of the barrel or its metallic appurtenances 
 and the conductor joined at the outer end of F. 
 
 The jacketed part of the barrel is further enveloped by a 
 spacious brass cylinder filled with ice or charged with water 
 kept in circulation and issuing from special auxiliary apparatus 
 adapted to secure constancy of temperature between and 
 about 50 0. Entering near the bottom, the circulating water 
 issues from a tubulure near the top. A thermometer shows its 
 temperature. Two stopcocks, seen at the bottom of the water- 
 jacket, facilitate influx. The bath is surrounded with wood 
 sawdust, contained between the four braced timbers of oak, 
 and kept in place by shutters not shown in the figure. The 
 upper part is protected with felting. 
 
 Details of Manipulation. Let the case of a liquid be first 
 considered. The piezometer, Fig. 4, clean and dry, is filled 
 with the liquid, which must have been boiled to remove the air 
 in the usual way. This done, a column of mercury several centi- 
 metres high is introduced at the lower end of the stern by aid 
 of a funnel, the end of which has been drawn out to as long 
 and fine a point as desirable. This end of the stem is then 
 plunged into a small glass full of mercury, and the body of the 
 piezometer carefully heated until the meniscus reaches the 
 lower end. On cooling the mercury again rises, and the 
 column so formed is very uniform and free from breaks due 
 to the other liquid. Thereafter the stem is provided with a 
 small cylindrical reservoir of steel, and the stem dips into the 
 E 65 
 
MEMOIRS ON 
 
 mercury contained as shown in the figure. It is now neces- 
 sary to find the mass of the liquid operated on. For this pur- 
 pose the piezometer is submerged in a long test-tube of glass 
 containing mercury at its lower end, into which the little steel 
 reservoir is plunged. A current of water at constant tempera- 
 ture is made to circulate in the test-tube, and when a state 
 of thermal equilibrium has been reached the volume of the 
 liquid is read off on a standardized scale etched into the lower 
 part of the stem. The piezometer may now be put into the 
 barrel of the pressure apparatus, also charged at its bottom 
 with a sufficient quantity of mercury. The electric circuit is 
 then completed, a spring-stop added to hold the piezometer in 
 place, the attachments for the production of pressure screwed 
 on, and all is now ready for making a series of measurements. 
 
 In the case of gases, the following operations are necessary: 
 The current of gas is passed into the piezometer, perfectly dry, 
 and heated from time to time during the operation, and passed 
 out through the fine point at the top. At suitable periods a 
 sample of the gas is tested, and when the examination shows 
 that the piezometer contains perfectly pure gas only, the point 
 at the top is closed with the blow-pipe. Thereafter, without 
 separating the piezometer from the purifying and drying train 
 in which a small excess of pressure is kept in action, the pie- 
 zometer is received and held vertically by a tube of brass in a 
 special apparatus, which in turn is submerged in a glass trough 
 supplied with a current of circulating water. When the tem- 
 perature has become stationary, the normal pressure is again 
 established in the dissicating trains, and the rubber tube con- 
 necting this apparatus with the lower end of the piezometer, 
 which alone is outside of the bath, is removed with caution. 
 At the same time this end is plunged into a cistern of mer- 
 cury. This operation to be well made requires some skill and 
 practice. It is now only necessary to fit the small steel thimble 
 to the lower end under mercury, and to place the piezometer 
 in the barrel. All heating which may cause the gas to flow 
 out during the adjustment is to be scrupulously avoided. It 
 is obvious that the pressure of the barometer was taken at 
 the required time, and that the mass of gas is thus perfectly 
 determinate. 
 
 All piezometers, whether adapted for liquids or for gases, were 
 calibrated with mercury in such a way that the instant at which 
 
THE LAWS OF GASES 
 
 the mercury touches one of the lateral platinum filaments of 
 the tube is shown electrically precisely in the manner to be 
 adopted during the experiments. The volumes given by the 
 calibration tables are therefore quite identical with the corre- 
 sponding measurements under pressure. 
 
 For the gas piezometers, in particular, this standardization is 
 a rather delicate operation because of the small volumes to be 
 measured. I carried it out in two ways, directly in weight and 
 indirectly in volume. By aid of a standard tube calibrated with 
 great care and temporarily soldered to the stem carrying the 
 platinum contacts, I measured the volume of mercury which 
 is withdrawn from this stem while the column is made to glide 
 from one contact to'the next. In this case the- small olive- 
 shaped reservoir just below the upper point is calibrated sepa- 
 rately. The point, though very fine, is itself calibrated from 
 a fiducial mark onward, in order that the diminution of volume 
 produced when the fine point is cut off and resoldered may be 
 estimated, however small it may be. 
 
 Plan of a Series of Measurements 
 
 Fig. 5 shows the completed apparatus and its accessories. 
 In the rear of the figure is the tank containing the water to be 
 heated. Constancy of temperature is obtained by the aid of a 
 crown burner of gas, a regulator, an influx tap, and an over- 
 flow, all conveniently disposed. For the lower temperatures, 
 water cooled down as far as zero in a refrigerator is raised to 
 any desired degree of temperature by its passage through longer 
 or shorter spirals kept within appropriate temperature baths. 
 On the left is seen the large force-pump communicating with 
 the corresponding stopcock and coupling. Quite in front is 
 the free-piston manometer with the lower end of the mercury 
 column. At the right, on a bracket, is the galvanometer, in- 
 serted into the electric circuit to announce the galvanic con- 
 tacts. It is seen at once how the first instant of contact is 
 obtained. For the others I adopted the following arrange- 
 ment : The current is branched and the galvanometer mounted 
 differentially. One of the shunts passes through the resistances 
 of the piezometer, a box of resistances, and a rheostat. The 
 galvanometer is put back to zero after each contact, and these 
 are unmistakably indicated by the suppression of a definite 
 quantity of piezometer resistance whenever the contact is 
 
 67 
 
MEMOIRS ON 
 
 made. The force-pump is first to be actuated in order to 
 completely fill the apparatus and to start the excess of internal 
 
 FIG. 5. DISPOSITION OF APPARATUS FOR VKRY HIGH PUKSSUUKS 
 
 pressure. To find the exact instant of contact use is made 
 of the compressing screw,, which, moreover, is employed ex- 
 
 68 
 
THE LAWS OF GASES 
 
 clusively as soon as the pressures reach values of 400 to 500 
 atmospheres. 
 
 When a contact is obtained it is necessary that the apparatus 
 should return again to its initial temperature, since this has 
 been changed by the thermal effect of compression. The 
 initial conditions may be considered as established when, on 
 breaking and reproducing the contact many times by means of 
 small pressure increments slowly applied, it is found to recur 
 uniform! vat the same pressure. This pressure is then marked 
 with a fine chalk pencil on the scale of the mercurial column. 
 The galvanometer is now set back to zero, while the compres- 
 sion is continued as far as the next contact, progressing in like 
 manner until the last contact is reached. Thereafter the series 
 is repeated throughout in the opposite direction i.e., all con- 
 tacts are passed again in a march of decreasing pressures. 
 
 If the series has been carried to completion rather too rapid- 
 ly, it will happen, owing to the inverse thermal effects during 
 the periods of increasing and decreasing pressures, that the 
 pressures observed in descending will be a little smaller, caet. 
 par., than those observed in ascending. The difference is 
 usually very small, and the mean may be taken. Its value at 
 the same time is a criterion of the degree of accuracy guaran- 
 teed. 
 
 When the constancy of temperature in the apparatus has 
 been exceptionally good, and if the observer has waited long 
 enough at each contact, the pressures in the ascending series 
 are exactly reproduced by the corresponding pressures in the 
 descending series. This is the best proof which can be given 
 of the trustworthiness of the instrument used in measuring 
 pressures. 
 
 Work may be done more expeditiously by completely sub- 
 merging the piezometer in mercury. The thermal effect of 
 compression is then small, and by reason of the good condition 
 of mercury, the thermal equilibrium is re-established very 
 quickly. In this case, however, the insulation of the resist- 
 ances requires much greater care. 
 
 When the cylinder and the piezometer are filled with water 
 it is perfectly feasible to put in evidence the reversal of the 
 thermal effect of compression on the respective sides of the 
 temperature of maximum density of water. 
 
 These operations, which require the concerted observation of 
 
MEMOIRS ON 
 
 at least three persons, are long and tedious. A single series 
 may extend over two, three, four hours, or even more, depend- 
 ing on the number of contacts and supposing that no accident 
 occurs. 
 
 I stated above that the prolongation of the unjacketed 
 breech of the steel cylinder seemed to be of excessive length. 
 The reason of this design may be found in an accident which 
 happened to me in the experiments in which oxygen was com- 
 pressed as far as a maximum density above 1.25 (relative to 
 water) at the temperature of 17 C. The cylinder was quite 
 strong and filled with mercury.* Suddenly, with a strident 
 noise, a jet of pulverulent mercury was hurled across the right 
 section of the breech, striking the base of the apparatus, re- 
 bounding thence to more than a metre in height in all direc- 
 tions. The noise was like that produced by a jet of steam 
 
 escaping from a boiler under high pressure. A right section 
 
 of the column after being polished showed nothing in particu- 
 lar when examined under the microscope. "We have thus en- 
 countered the classical experiment of the rain of mercury 
 through the pores of a body of steel about .08 metre thick. 
 The pressure was certainly as high as 4000 atmospheres. The 
 same apparatus under the same pressure did not admit of the 
 exudation of a single drop of glycerine. It would doubtless 
 have shown the same negative result for water and for other 
 liquids. 
 
 J^o similar accident occurred during the course of my work, 
 so far as a flow normal to the section of the cylinders used is 
 concerned. The reason why the thickness of the breech was 
 increased to an extreme degree in the direction of the axis is, 
 therefore, clear. 
 
 I was induced to devise a jacketed cylinder in consequence 
 of an accident of another kind. The first large cylinder of 
 steel which I used (weighing 116 kg.) split apart along opposite 
 generatrices throughout a considerable part of its length. Al- 
 though there was neither projection nor separation of parts, 
 nor any sudden issue of gas, the rupture was nevertheless ac- 
 companied with a detonation of extreme violence. During a 
 few moments the mercury escaped from the fissure, and I bad 
 time to observe it in form of .a bright metallic plate 6 to 7 cen- 
 
 *-Cvmpt8 RendiiH. March 2, 1885. 
 70 
 
THE LAWS OF GASES 
 
 timetres in breadth. It was owing to the occurrence of these 
 two accidents that I added the steel jacket to the cylinder, as 
 already described. 
 
 3. APPARATUS FOR HIGHER TEMPERATURES 
 
 Method of Sights. 
 
 It would be difficult to work at temperatures markedly higher 
 than those for which the apparatus just described was designed. 
 The mass of the jacketed steel barrel, the presence of the ap- 
 pliances added at its top and which project outside of the bath, 
 would make a uniform degree of high temperature very diffi- 
 cult of attainment. The joints and the cap-shaped washer 
 would no longer insure freedom from leakage. Finally and 
 particularly, for the case of gases, the piezometer stems, fragile 
 at best by reason of the inserted platinum filaments, would be- 
 come prohibitively so, while the difficulties of an adequate in- 
 sulation of the parts would in like measure greatly increase. 
 
 The following design, which I shall call the method of sights 
 (methode des regards), has enabled me to work as far as 360 C. 
 It would even be possible to reach higher temperatures, in 
 modifying the apparatus in the way which experience has 
 suggested, but which I do not expect to apply at present. I 
 have also thought it desirable to restrict the pressures within 
 1000 atmospheres, although in many trials I went much beyond 
 this. 
 
 The method may expediently be described together with the 
 apparatus. The latter is represented in sectional elevation in 
 Fig. 6. In the lower part of the apparatus the jacketed 
 barrel, HH, of the preceding compressor will be recognized, 
 although three breaks were needed to shorten the figure. At 
 the top of this is fixed (as above) the apparatus for producing 
 pressure, modified by the introduction of a cross of steel, 
 A, A, F, F, forged and thereafter turned and pierced at the 
 lathe throughout the axis of the arms. The horizontal arm, 
 AA, carries the bolts, BB, screwed to its two extremities, 
 suitably tubulated, in which the sights are cemented with 
 marine glue. These are small cylinders of crown glass or of 
 quartz, with good plane parallel faces, about 1 centimetre in 
 diameter and 2 centimetres long. The joint with the gland is 
 
 71 
 
MEMOIRS ON 
 
 4> 
 
 S I 
 J 
 
 FIG. 6. APPARATUS FOR THE METHOD OF SIGHTS. 
 FIG. 7. PIEZOMETER FOR LIQUIDS. 
 FIG. 8. PIEZOMETER FOR GASES. 
 
 72 
 
THE LAWS OF GASES 
 
 sealed with a washer of celluloid. The piezometer is mounted 
 symmetrically with the axis of the apparatus, and the figure 
 shows a piezometer of gas in place. Its reservoir is submerged 
 in mercury, which now partially fills the barrel. Its very long 
 stem terminates above in a small olive-shaped reservoir ending 
 in a fine point, as above. Below the enlargement is the gradu- 
 ation, about 25 centimetres long and made of very delicate cir- 
 cular marks narrowing towards the top. Little globular ex- 
 pansions were blown out between them along the lower part of 
 the stem, with the object of virtually increasing the total 
 length of the graduated part. The piezometer is suspended 
 from its upper end by aid of a small pad which is attached to 
 it under the uppermost bulb, and sustained by the aid of a 
 device, BB, CO, shown enlarged in a separate figure. This 
 piece is connected at CC to an intermediate stem of glass 
 joined in the same way at its upper extremity to a long rod of 
 steel. The latter, after having traversed a stuffing-box charged 
 with leather washers, is in its turn joined to the lower end of a 
 long steel screw. This is movable in a socket of brass carried 
 by the same coupling which receives the leather of the stuffing- 
 box. The jacketed barrel, part of the barrel HH, is as usual 
 provided with a stopcock (not shown), through which the in- 
 itial pressures are applied in virtue of the force-pump. An- 
 other tube communicates with the manometer. In place of the 
 third coupling, which, in the former case, supplied the electric 
 current, there is now a tube of steel leading to a special steel 
 reservoir, to which the device for producing pressure, former- 
 ly described, is suitably attached. High pressure is, therefore, 
 brought to bear at this place by manipulating the lower screw. 
 
 The method of experimentation will now be intelligible 
 without much further explanation. By means of the screw at 
 the top of the apparatus, the division -rings on the stem of 
 the piezometer are successively placed in the line of sight. 
 Thereupon pressure is applied until the meniscus appears 
 flush with the division mark, and this pressure is registered. 
 The readings are made with a reading telescope well centred 
 in the line of sight, and the field of vision is illuminated with a 
 simple gas-lamp placed on the opposite side in the same direc- 
 tion. This light is quite sufficient as long as certain precau- 
 tions are taken which I will now indicate. The injection water 
 rapidly loses its transparency, particularly when the stem is 
 
 73 
 
MEMOIRS ON 
 
 heated. Keading thus becomes more impossible in proportion 
 as the layer of liquid penetrated by the rays is thicker. To 
 obviate this difficulty I at first placed cylinders of crown-glass, 
 plane-parallel and perfectly transparent, throughout the whole 
 length of the channel. Readings at the lower temperatures 
 were then easily made, but at the higher temperatures the 
 faces of the glass cylinder were rapidly attacked in the hot re- 
 gions and after a time covered over with an opaque pulverulent 
 layer, being thus completely corroded. Hence, in subsequent 
 work I replaced the crown-glass cylinders in the hot parts of 
 the tube by quartz cylinders with their faces normal to the 
 axis. Readings could then be made without difficulty. Again, 
 to avoid the decomposition of leather, which would have 
 clouded the internal faces of the sight-cylinders, the joints in 
 the nuts and valves were sealed with celluloid washers. 
 
 The different temperatures at which it was proposed to in- 
 vestigate were obtained by enveloping the arms of the cross, 
 AF, by an appliance adapted to do service either as a water- 
 bath or as a vapor-bath. The lower part of this surrounded 
 the three arms permanently, the seal being made with red-lead. 
 The upper part of the bath differed in form according to the 
 uses to be made of it, and it was fitted into a shouldered rim 
 in the lower part and held in place by friction. 
 
 To obtain a vapor-bath an appliance with a two-chambered 
 interior was at hand, provided with a perforated bottom. The 
 condenser communicated with the tubulure F of the removable 
 lid, which at the same time furnished a support for the ther- 
 mometers. When a liquid bath was wanted, the partition was 
 replaced by an agitator actuated by a small Gramme machine. 
 Constancy of temperature was then obtained by suitably ad- 
 justing the distance and the gas supply of the crown burner 
 seen at the bottom of the bath. 
 
 At D, under the leather stuffing-box, and at the extremities, 
 BB, of the horizontal arms, small water- jackets were added, 
 fed with a current of cold water. This prevented serious over- 
 heating of the leather washers or of the mastic seals at the 
 sights. The discharge water flows into the lower reservoir, 
 keeping the joints of the cross, which are plunged in it, cold, 
 and then escapes by a lateral tubulure. 
 
 The result of this cooling is that under the stuffing-box, G, 
 m particular, the cross reaches the temperature of the bath 
 
 74 
 
THE LAWS OF GASES 
 
 only at a considerable distance below the lid. I thought it 
 worth while to make direct tests by using long, probelike ther- 
 mometers specially made for this purpose, in order to be prop- 
 erly guided as to the maximum height up to which the tip of 
 the piezometer could be raised at any temperature without en- 
 countering seriously reduced values. It would have been far 
 preferable indeed, at higher temperatures, it would be abso- 
 lutely necessary to close the cross immediately below the 
 stuffing-box, and to produce the vertical displacement of the 
 piezometer by means of an appropriate appliance attached at 
 the lower end. All this is feasible, though not without diffi- 
 culty. 
 
 PRELIMINARY OPERATIOXS 
 
 After what has been said relatively to the first method, only 
 a few words are needed. The piezometers, Figs. 7 and 8, both 
 for liquids and for gases, do not differ from those above de- 
 scribed except as to the stems, which now carry the circular 
 division marks in place of the platinum filaments formerly used. 
 They are filled and the mass of the contents determined in 
 identically the same way as before, but it is much more difficult 
 to adjust them in place. This can only be done by a suitable 
 pulley-block fastened to the ceiling, by means of which the cross 
 may be raised or lowered without the least jolting. Even slight 
 percussion would invariably break the stem of the piezometer. 
 
 Constancy of temperature is now reached much more rapidly 
 than in the preceding experiments, whether the environment 
 be an ice-bath, a water or a vapor bath ; for the total mass 
 which is to reach a stationary temperature distribution is 
 enormously smaller. A full series of experiments is neverthe- 
 less tediously prolonged, seeing that the number of division 
 marks on the stem is so much larger than the number of plati- 
 num filaments above. As far as 100 the temperatures were 
 given by water-baths. A point very near 200 corresponds to 
 the boiling-point of methyl benzoate, another at 260 to amyl 
 benzoate. Many bodies were tested as to their availability in 
 vapor-baths between 100 and 200. For 140 I employed 
 xylene and ethyl acetate, but the results were less satisfactory 
 than in the preceding cases. I was quite unable to obtain a 
 perfectly constant temperature from xylene. The specific 
 heat per unit of volume seems to be very small, and the heat 
 
 75 
 
MEMOIRS ON 
 
 transferred insufficient to compensate for the external losses. 
 I shall therefore publish the series made at this temperature 
 with this special reservation. 
 
 In all the series of measurements made up to 100 by this 
 method, I restricted the observations to an exact number of 
 degrees, using thermometers for this purpose compared in ad- 
 vance with a standard provided by the Bureau International 
 des Poids et Mesures, and calibrated by M. Guillaume. They 
 are reduced to the hydrogen thermometer by means of the 
 table of M. Ohappuis. At 100 either a water-bath or a steam- 
 bath was available. I have given the results for 100 exactly, 
 the interpolation being insignificant and no error resulting from 
 it. Temperatures above 100 were determined by means of ex- 
 cellent thermometers of hard glass, constructed by M. Chabaud, 
 who also made the piezometers. A preliminary comparison of 
 these instruments with the hydrogen thermometer showed only 
 very small differences, for which allowance was made through- 
 out. There is no room here to give the data for this calibra- 
 tion, as I had hoped to do; but I took into account the displace- 
 ment of the zero mark by applying a special test .after each 
 series of measurements. The variations of this point were small. 
 
 However complicated the apparatus itself may appear, the 
 measurements are made with facility, barring accidents, of 
 course. The length of time consumed alone made them te- 
 dious. When a division mark has been brought into the field 
 of the telescope, pressure is applied until the mark is tangent 
 to the mercury meniscus, which here appears as a dark demar- 
 cation on a luminous background. The adjustment is easily 
 made on compressing with the screw, and this, as in the pre- 
 ceding work, was used exclusively whenever the pressures ex- 
 ceeded a high value. Unfortunately, at high temperatures the 
 action of the water eventually tarnishes the external surface 
 of the graduated stem, and the meniscus appears blurred. 
 Hence it is always necessary to stop after each series made at 
 the higher temperatures, and take the apparatus apart in order 
 to lightly repolish the stem. The operation is easily accom- 
 plished with the aid of a polishing wheel, mounted on a lathe. 
 The present corrosion, however, is not to be compared to simi- 
 lar experiences with crown-glass mentioned above. It is for 
 this reason that hard glass piezometers were selected. 
 
 Pressures are measured in the way described above. Ob- 
 
 76 
 
THE LAWS OF GASES 
 
 viously, account must be taken of the temperature of the mer- 
 cury column, of the height of the mercury in the piezometer 
 above its level in the barrel, and of the position of this level 
 relatively to the manometer. 
 
 The measurement of small volumes is one of the difficulties 
 of these researches. Without entering into any detail, I will 
 simply state that allowance was made for the form of the me- 
 niscus, and of its position with reference to the division mark 
 during calibration and during the subsequent measurements. 
 Only in the case of gases are the errors here in question to be 
 apprehended. Their volumes diminish with extreme rapidity, 
 even when the reservoirs are made as large as is compatible 
 with the dimensions of the barrel. 
 
 PART II. DATA FOR GASES 
 
 The results summarized by the following tables were ob- 
 tained in experiments of the kind just described. 
 
 After adding all corrections, the pressures were first ex- 
 pressed in atmospheres. To find the corresponding volumes, 
 the piezometer may be supposed to be standardized at C., 
 seeing that volume ratios alone are in question. Account must 
 be taken, however, when necessary, of the temperature differ- 
 ences occurring when the different parts of the piezometer (stem 
 and reservoir) were calibrated. The corrections due to thermal 
 expansion and to compression were afterwards applied in their 
 turn. In my former researches I have given all the necessary 
 data. 
 
 Having found the mass of the fluid in the manner stated 
 above, and recalling that the calibration is supposed to be cor- 
 rect at zero, all the subsequent volumes are reduced to the 
 value they would have if the given mass were that of unit of 
 volume at C. and 1 atmosphere. My tables, without excep- 
 tion, refer to this unit. Thereafter I constructed a series of 
 curves corresponding to my data, in which pressures are the 
 abscissas and the products, P V, of pressure and volume the 
 ordinates. From these curves I selected a series of correlated 
 values of PV, corresponding to groups of pressures differing 
 in round numbers by 25, 50, or 100 atmospheres, and from them 
 I deduced the values of V. For carbon dioxide and ethylene 
 I batched the data in smaller pressure intervals because of the 
 
 77 
 
MEMOIRS ON 
 
 complex form of curve observed in the region of the critical 
 point. Supplementary tables are here given. 
 
 The data for the pressure coefficient are taken directly from 
 the curves. It sufficed to draw the lines of equal volume, 
 which, under present circumstances, are straight lines passing 
 through the origin, and then to read off the pressures at which 
 these lines cut the successive isotherms. The curves were 
 drawn either as a whole or by distributing them on sheets of 
 millimetre cross-section paper, stretched on a large drawing- 
 board more than 2 meters broad. 
 
 The gases studied are oxygen, hydrogen, nitrogen, air, car- 
 bon dioxide, and ethylene. The last were operated on by the 
 method of sights only ; the other gases by both methods. 
 
 RESULTS OBTAINED BY THE FIRST METHOD 
 
 (Method of Electric Contacts) 
 
 I will begin with the results of the first method. The num- 
 bers relating to pressures below 500 atmospheres belong to the 
 series of data obtained by the second method. The series 
 found by the method of contacts does not begin until above 
 500 or 600 atmospheres. The other results are reproduced 
 here so as to give completed series at zero. 
 
 TABLE 4 
 
 
 OXYGEN 
 
 C. C. 
 
 15.6 C. 
 
 HYDR 
 
 C. QO C. 
 
 OGEN 
 
 15.4 C. 
 
 47.30 C. 
 
 p 
 
 PV 
 
 FX10 
 
 FX106 
 
 PV 
 
 FX 106 
 
 FX 106 
 
 FxlOe 
 
 Aim. 
 
 
 
 
 
 
 
 
 1 
 
 1.0000 
 
 10 6 
 
 
 
 1 0000 
 
 10 6 
 
 
 
 
 
 100 
 
 .9265 
 
 9265 
 
 
 
 1.0690 
 
 10690 
 
 
 
 
 
 200 
 
 .9140 
 
 4570 
 
 
 
 1.1380 
 
 5690 
 
 
 
 
 
 300 
 
 .9625 
 
 3208 
 
 
 
 1 2090 
 
 403000 
 
 
 
 
 
 400 
 
 1.0515 
 
 2629 
 
 
 
 1.2830 
 
 320700 
 
 
 
 
 
 500 
 
 1.1570 
 
 2314 
 
 
 
 1.3565 
 
 271300 
 
 
 
 
 
 600 
 
 1.2702 
 
 2117 
 
 2228 
 
 1.4322 
 
 2387 
 
 
 
 
 
 700 
 
 1.3867 
 
 1981 
 
 2075 
 
 1.5050 
 
 2150 
 
 2234 
 
 
 
 800 
 
 1.5040 
 
 1880 
 
 1959 
 
 1.5760 
 
 1970 
 
 2046 
 
 
 
 900 
 
 1.6200 
 
 1800 
 
 1871 
 
 1.6515 
 
 1835 
 
 1895 
 
 _ 
 
 1000 
 
 1.7360 
 
 1736 
 
 1800 
 
 1.7250 
 
 1725 
 
 1778 
 
 1893 
 
 1100 
 
 1.8502 
 
 1682 
 
 1740 
 
 1.8007 
 
 1637 
 
 1685 
 
 1785 
 
 1200 
 
 1.9620 
 
 1635 
 
 1689 
 
 1.8690 
 
 1557.5 
 
 1604 
 
 1694.5 
 
 1300 
 
 2.0722 
 
 1594 
 
 1645 
 
 1.9383 
 
 1491 
 
 1533 
 
 1617.5 
 
 1400 
 
 2.1798 
 
 1557 
 
 1605 
 
 2.0048 
 
 1432 
 
 1472 
 
 1551 
 
 1500 
 
 2.2890 
 
 1526 
 
 1571 
 
 2.0700 
 
 1380 
 
 1418 
 
 1493 
 
 1600 
 
 2.3960 
 
 1497.5 
 
 1540 
 
 2.1352 1334.5 
 
 1370 
 
 1442 
 
 1700 
 
 2.5024 
 
 1472 
 
 1513.5 
 
 2.20065 
 
 1294.5 
 
 1326 
 
 1396 
 
 78 
 
THE LAWS OF GA 
 
 TABLE 4. Continued 
 
 OXYGEN 
 
 HYDROGEN 
 
 
 C. C. 
 
 15. 6 C. 
 
 QO C. C. 
 
 15. 4 C. 
 
 47.3 C. 
 
 P 
 
 PV 
 
 FXlO* 
 
 FX106 
 
 PV 
 
 FX106 
 
 FX 10 
 
 FX106 
 
 Atm. 
 
 
 
 
 
 
 
 
 1800 
 
 2.6073 
 
 1448.5 
 
 1488.5 
 
 2.2644 
 
 1258 
 
 1288 
 
 1354 
 
 1900 
 
 2.7113 
 
 1427 
 
 1465 
 
 2.3275 
 
 1225 
 
 1254.5 
 
 1316 
 
 2000 
 
 2.8160 
 
 1408 
 
 1444 
 
 2.3890 
 
 1194.5 
 
 1222.5 
 
 1280.5 
 
 2100 
 
 2.9190 
 
 1390 
 
 1424 
 
 2.44965 
 
 1166.5 
 
 1194 
 
 1249 
 
 2200 
 
 3.0217 
 
 1373.5 
 
 1406 
 
 2.5102 
 
 1141 
 
 1168.5 
 
 1220 
 
 2300 
 
 3. 1234 
 
 1358 
 
 1390 
 
 2.5714 
 
 1118 
 
 1144.5 
 
 1194.5 
 
 2400 
 
 3.2244 
 
 1343.5 
 
 1374 
 
 2.6340 
 
 1097.5 
 
 1122.5 
 
 1170.5 
 
 2500 
 
 3.32375 
 
 1329.5 
 
 1360 
 
 2.6950 
 
 1078 
 
 1101 
 
 1148 
 
 2600 
 
 3.4229 
 
 1316.5 
 
 1346 
 
 2.7547 
 
 1059.5 
 
 1082.5 
 
 1126.5 
 
 2700 
 
 3.5208 
 
 1304 
 
 1332 
 
 2.8134 
 
 1042 
 
 1063 
 
 1107 
 
 2800 
 
 3.6176 
 
 1292 
 
 1319.5 
 
 2.8686 
 
 1024.5 
 
 1045 
 
 1088 
 
 2900 
 
 3.7120 
 
 1280 
 
 1307 
 
 
 
 
 
 1028 
 
 1071 
 
 3000 
 
 
 
 
 
 1296 
 
 
 
 
 
 1012.8 
 
 
 
 TABLE 5 
 
 NITKOGE 
 C. C. 
 
 N 
 16.0 C. 
 
 43. 6 C. 
 
 A 
 C. C. 
 
 IR 
 
 15. 7 C. 
 
 45.10C. 
 
 PV 
 
 FX io 
 
 FX106 
 
 FX 106 
 
 PV 
 
 FX 106 
 
 FX 106 
 
 FX 106 
 
 1.0000 
 
 10 6 
 
 
 _ 
 
 1.0000 
 
 10 6 
 
 
 
 .9910 
 
 9910 
 
 
 
 
 
 .9730 
 
 9730 
 
 
 
 
 
 1.0390 
 
 5195 ' 
 
 
 
 
 
 1.0100 
 
 5030 
 
 
 
 
 
 1.1360 
 
 3786 
 
 
 
 
 
 1.0975 
 
 3658 
 
 
 
 
 
 1.2570 
 
 3142 
 
 
 
 
 
 1.2145 
 
 3036 
 
 
 
 
 
 1.3900 
 
 2780 
 
 
 
 
 
 1.3400 
 
 2680 
 
 
 
 
 
 1.5260 
 
 2543 
 
 
 
 
 
 1.4700 
 
 2450 
 
 
 
 
 
 1.6625 
 
 2375 
 
 
 
 
 
 1.6037 
 
 2291 
 
 2384 
 
 
 
 1.8016 
 
 2252 
 
 2331 
 
 
 
 1.7368 
 
 2171 
 
 2251.5 
 
 2387.5 
 
 1.9368 
 
 2152 
 
 2224 
 
 2354 
 
 1.8675 
 
 2075 
 
 2147 
 
 2271 
 
 2.0700 
 
 2070 
 
 2134 
 
 2242 
 
 1.9990 
 
 1999 
 
 2061.5 
 
 2176.5 
 
 2.20385 
 
 2003.5 
 
 2062 
 
 2162 
 
 2.1329 
 
 1939 
 
 1992 
 
 2097 
 
 2.3352 
 
 1946 
 
 2000 
 
 2095 
 
 2.2596 
 
 1883 
 
 1933 
 
 2030 
 
 2.46545 
 
 1896.5 
 
 1945 
 
 2035 
 
 2.3842 
 
 1834 
 
 1880 
 
 1970 
 
 2.5942 
 
 1853 
 
 1897 
 
 1982 
 
 2.5081 
 
 1791.5 
 
 1834 
 
 1917 
 
 2.72025 
 
 1813.5 
 
 1854 
 
 1933 
 
 2.6310 
 
 1754 
 
 1793.5 
 
 1871.5 
 
 2.8456 
 
 1778.5 
 
 1818 
 
 1891.5 
 
 2.7528 
 
 1720.5 
 
 1757 
 
 1832.5 
 
 2.9665 
 
 1745 
 
 1784 
 
 1853.5 
 
 2.87385 
 
 1690.5 
 
 1725 
 
 1796.5 
 
 3.0861 
 
 1714.5 
 
 1752 
 
 1817.5 
 
 2.9916 
 
 1662 
 
 1695 
 
 1762.5 
 
 3.20815 
 
 1688.5 
 
 1724.5 
 
 1787.5 
 
 3.1103 
 
 1637 
 
 1668 
 
 1733 
 
 3.3270 
 
 1663.5 
 
 1699 
 
 1758.5 
 
 3.2260 
 
 1613 
 
 1643 
 
 1705 
 
 3.4461 
 
 1641 
 
 1675 
 
 1731.5 
 
 3.34005 
 
 1590.5 
 
 1629 
 
 1678.5 
 
 3.5640 
 
 1620 
 
 1653 
 
 1707 
 
 3.4540 
 
 1570 
 
 1598 
 
 1654 
 
 3.6823 
 
 1601 
 
 1632 
 
 1683.5 
 
 3.56615 
 
 1550.5 
 
 1578 
 
 1632.5 
 
 38004 
 
 1583.5 
 
 1613.5 
 
 1663.5 
 
 3.6804 
 
 1533.5 
 
 1559.5 
 
 1612 
 
 3.9200 
 
 1568 
 
 1596 
 
 1644 
 
 379125 
 
 1516.5 
 
 1542 
 
 1593.5 
 
 4.0378 
 
 1553 
 
 1579 
 
 1626 
 
 3.9000 
 
 1500 
 
 1525 
 
 1575.5 
 
 4.1553 
 
 1539 
 
 1564 
 
 1608 
 
 4.00815 
 
 1484.5 
 
 1510 
 
 1557.5 
 
 4.2700 
 
 1525 
 
 1549.5 
 
 1592 
 
 4.1146 
 
 1469.5 
 
 1495 
 
 1541 
 
 4 3558 
 
 1502 
 
 1536 
 
 1577 
 
 42195 
 
 1455 
 
 1480.5 
 
 1525 
 
 4.4970 
 
 1499 
 
 1522.5 
 
 1563 
 
 43230 
 
 1441 
 
 1466 
 
 1509.5 
 
 Atm. 
 
 1 
 
 100 
 
 200 
 
 300 
 
 400 
 
 500 
 
 600 
 
 700 
 
 800 
 
 900 
 
 1000 
 
 1100 
 
 1200 
 
 1300 
 
 1400 
 
 1500 
 
 1600 
 
 1700 
 
 1800 
 
 1900 
 
 2000 
 
 2100 
 
 2200 
 
 2300 
 
 2400 
 
 2500 
 
 2600 
 
 2700 
 
 2800 
 
 2900 
 
 3000 
 
 79 
 
MEMOIRS ON 
 
 The following tables contain the data needed for the calcula- 
 tion of the pressure coefficients. They show the pressures at 
 which the unit of mass occupies the volumes given in the first 
 column at the stated temperatures : 
 
 TABLE 6. PRESSURES AT CONSTANT VOLUME 
 
 CONSTANT 
 VOLUME 
 
 OXYGEN 
 0C. 
 
 15. 6 C. 
 
 CONSTANT 
 VOLUME 
 
 HYDRC 
 
 oc. 
 
 >GEN 
 
 15.4 C. 
 
 47.3 C. 
 
 FxlO 6 
 2117 
 1880 
 1736 
 1635 
 1497.5 
 1408 
 1343.5 
 1304 
 
 Aim. 
 600 
 800 
 1000 
 1200 
 1600 
 2000 
 2400 
 2700 
 
 Aim. 
 669 
 888 
 1106 
 1325 
 1765 
 2188 
 2618 
 2925 
 
 FxlO 6 
 1725 
 1557.5 
 1380 
 1258 
 1194.5 
 1097.5 
 1024.5 
 
 Aim. 
 1000 
 1200 
 1500 
 1800 
 2000 
 2400 
 2800 
 
 Aim,: 
 1055 
 1264 
 1579 
 1889 
 2099 
 2518 
 1925 
 
 Atm. 
 1164 
 1390 
 1737 
 2071 
 2300 
 2746 
 
 CONSTANT 
 VOLUME 
 
 NITRO< 
 
 0('. 
 
 ^EN 
 
 16.0 C 
 
 43.6 C. 
 
 CONSTANT 
 VOLUME 
 
 All 
 
 oc. 
 
 i 
 
 15.7 C. 
 
 45.1 C. 
 
 FxlO 6 
 
 Atm. 
 
 Atm. 
 
 Atm. 
 
 FxlO 6 
 
 Atm. 
 
 Atm. 
 
 Atm. 
 
 2070 
 
 1000 
 
 1088 
 
 1239 
 
 2171 
 
 800 
 
 876 
 
 1007 
 
 1946 
 
 1200 
 
 1298 
 
 1474 
 
 1999 
 
 1000 
 
 1089 
 
 1250 
 
 1813.5 
 
 1500 
 
 1613 
 
 1812 
 
 1883 
 
 1200 
 
 1295 
 
 1474 
 
 1714.5 
 
 1800 
 
 1937 
 
 2168 
 
 1754 
 
 1500 
 
 1610 
 
 1828 
 
 1663.5 
 
 2000 
 
 2150 
 
 2401 
 
 1662 
 
 1800 
 
 1924 
 
 2166 
 
 1583.5 
 
 2400 
 
 2572 
 
 2858 
 
 1613 
 
 2000 
 
 2131 
 
 2394 
 
 1525 
 
 2800 
 
 2990 
 
 
 
 1533.5 
 
 2400 
 
 2552 
 
 2846 
 
 RESULTS OBTAINED BY THE SECOND METHOD 
 
 (Method of Sights) 
 
 The following tables of results obtained by the second 
 method are arranged like the preceding, except that only the 
 products P V are given for all the series : 
 
 80 
 
THE LAWS OF GASES 
 
 TABLE 7. OXYGEN" 
 
 Atm. 
 1 
 
 100 
 150 
 200 
 250 
 300 
 350 
 400 
 450 
 500 
 550 
 600 
 650 
 700 
 750 
 800 
 850 
 900 
 950 
 1000 
 
 oc. 
 
 15.65 C. 
 
 99.500 C. 
 
 199.50 c. 
 
 PV 
 
 FX106 
 
 PV 
 
 FX106 
 
 PV 
 
 Fxios 
 
 PV 
 
 FXIO 
 
 1.0000 
 
 10 6 
 
 
 
 
 
 
 
 .9265 
 
 9265 
 
 1.0045 
 
 10045 
 
 1.3750 
 
 13750 
 
 
 
 
 
 .9135 
 
 6090 
 
 .9920 
 
 6613 
 
 1.3820 
 
 9213 
 
 1.8000 
 
 12000 
 
 .9140 
 
 4570 
 
 .9945 
 
 4972 
 
 1.4000 
 
 7000 
 
 1.8190 
 
 9095 
 
 .9315 
 
 3726 
 
 1.0135 
 
 4054 
 
 .4240 
 
 5696 
 
 1.8500 
 
 7400 
 
 .9625 
 
 3208 
 
 1.0420 
 
 3473 
 
 .4530 
 
 4843 
 
 1.8850 
 
 6283 
 
 1 0040 
 
 2869 
 
 1.0800 
 
 3086 
 
 .4900 
 
 4257 
 
 1.9220 
 
 5491 
 
 1.0515 
 
 2629 
 
 1.1250 
 
 2812 
 
 .5320 
 
 3830 
 
 1.9610 
 
 4902 
 
 1.1025 
 
 2450 
 
 1.1750 
 
 2611 
 
 .5760 
 
 3502 
 
 2.0040 
 
 4453 
 
 1.1560 
 
 2312 
 
 1.2270 
 
 2454 
 
 .6220 
 
 3244 
 
 2.0500 
 
 4100 
 
 1.2120 
 
 2204 
 
 1.2815 
 
 2330 
 
 .6690 
 
 3035 
 
 2.0950 
 
 3809 
 
 1.2690 
 
 2115 
 
 1.3370 
 
 2228 
 
 .7200 
 
 2867 
 
 2.1420 
 
 3570 
 
 1.3275 
 
 2042 
 
 1.3940 
 
 2144 
 
 .7725 
 
 2727 
 
 2.1910 
 
 3371 
 
 1.3855 
 
 1979 
 
 1.4515 
 
 2073 
 
 .8270 
 
 2610 
 
 2.2415 
 
 3202 
 
 1.4440 
 
 1925 
 
 1.5080 
 
 2011 
 
 .8810 
 
 2508 
 
 22920 
 
 3056 
 
 1.5030 
 
 1879 
 
 1.5660 
 
 1957 
 
 .9340 
 
 2417 
 
 2.3430 
 
 2929 
 
 1.5615 
 
 1841 
 
 1 6240 
 
 1911 
 
 1.9875 
 
 2338 
 
 2.3950 
 
 2812 
 
 1.6200 
 
 1800 
 
 1.6820 
 
 1869 
 
 2.0415 
 
 2268 
 
 2.4465 
 
 2718 
 
 1.6780 
 
 1766 
 
 1.7400 
 
 1831 
 
 2.0960 
 
 2206 
 
 2.4980 
 
 2629 
 
 1.7355 
 
 1735 
 
 1.7980 
 
 1798 
 
 2.1510 
 
 2151 
 
 
 
 
 
 TABLE 8. HYDROGEN 
 
 p 
 
 oc. 
 
 15.50 C. 
 
 99.25C. 
 
 200. 25 C. 
 
 PV 
 
 Fxioe 
 
 PV 
 
 FX106 
 
 PV 
 
 FX106 
 
 PV 
 
 FX106 
 
 Atm. 
 
 
 
 
 
 
 
 
 
 1 
 
 1.0000 
 
 10 6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 100 
 
 1.0690 
 
 10690 
 
 1.1290 
 
 11290 
 
 
 
 
 
 
 
 
 
 150 
 
 1.1030 
 
 7353 
 
 1.1630 
 
 7753 
 
 1.4770 
 
 9846 
 
 1.8480 
 
 12320 
 
 200 
 
 1.1380 
 
 5690 
 
 1.1980 
 
 5990 
 
 1.5135 
 
 7567 
 
 1.8840 
 
 9420 
 
 250 
 
 1.1730 
 
 4692 
 
 1.2350 
 
 4940 
 
 1.5500 
 
 6200 
 
 1.9200 
 
 7680 
 
 300 
 
 12090 
 
 4030 
 
 1.2685 
 
 4228 
 
 1.5860 
 
 5286 
 
 1.9560 
 
 6520 
 
 350 
 
 1.2460 
 
 3560 
 
 1.3050 
 
 3728 
 
 1.6225 
 
 4636 
 
 1.9930 
 
 5694 
 
 400 
 
 .2830 
 
 3207 
 
 1.3410 
 
 3352 
 
 1.6590 
 
 4147 
 
 2.0300 
 
 5075 
 
 450 
 
 .3200 
 
 2933 
 
 1.3780 
 
 3062 
 
 1.6950 
 
 3766 
 
 2.0670 
 
 4593 
 
 500 
 
 .3565 
 
 2713 
 
 1.4150 
 
 2830 
 
 1.7310 
 
 3462 
 
 2.1050 
 
 4210 
 
 550 
 
 .3935 
 
 2533 
 
 1.4520 
 
 2640 
 
 1.7675 
 
 3214 
 
 2.1400 
 
 3891 
 
 600 
 
 .4315 
 
 2386 
 
 1.4890 
 
 2482 
 
 1.8040 
 
 3006 
 
 2 1762 
 
 3627 
 
 650 
 
 1.4685 
 
 2259 
 
 1.5260 
 
 2347 
 
 1.8400 
 
 2831 
 
 2.2120 
 
 3403 
 
 700 
 
 1.5045 
 
 2149 
 
 1.5620 
 
 2231 
 
 1.8760 
 
 2680 
 
 2.2480 
 
 3211 
 
 750 
 
 1.5400 
 
 2053 
 
 1.5985 
 
 2131 
 
 1.9130 
 
 2551 
 
 2.2840 
 
 3045 
 
 800 
 
 1.5775 
 
 1972 
 
 1.6340 
 
 2042 
 
 1.9490 
 
 2436 
 
 2.3200 
 
 2900 
 
 850 
 
 1.6140 
 
 1879 
 
 1.6690 
 
 1964 
 
 1.9860 
 
 2336 
 
 2.3560 
 
 2772 
 
 900 
 
 1.6490 
 
 1832 
 
 1.7060 
 
 1896 
 
 2.0210 
 
 2244 
 
 2.3915 
 
 2657 
 
 950 
 
 1.6850 
 
 1774 
 
 1.7410 
 
 1832 
 
 20660 
 
 2174 
 
 
 
 
 
 1000 1.7200 
 
 1720 
 
 1.7760 
 
 1776 
 
 2.0930 
 
 2093 
 
 
 
 
 
 81 
 
MEMOIRS ON 
 
 TABLE 9. NITROGEN 
 
 p 
 
 oc. 
 
 16.03 C. 
 
 99.45C. 
 
 199.500 C . 
 
 PV 
 
 Fxioe 
 
 PV 
 
 FXIO 
 
 PV 
 
 FX106 
 
 PV 
 
 FX10 
 
 Aim. 
 
 
 
 
 
 
 
 
 
 1 
 
 1.0000 
 
 10' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 100 
 
 .9910 
 
 9910 
 
 1.0620 
 
 10620 
 
 
 
 
 
 
 
 
 
 150 
 
 1.0085 
 
 6723 
 
 1.0815 
 
 7210 
 
 1.4500 
 
 9666 
 
 1.8620 
 
 12410 
 
 200 
 
 1.0390 
 
 5195 
 
 .1145 
 
 5572 
 
 1.4890 
 
 7445 
 
 1.9065 
 
 9532 
 
 250 
 
 1.0825 
 
 4330 
 
 .1575 
 
 4630 
 
 1.5376 
 
 6150 
 
 1.9585 
 
 7834 
 
 300 
 
 1.1360 
 
 3786 
 
 .2105 
 
 4035 
 
 1.5905 
 
 5301 
 
 2.0145 
 
 6715 
 
 350 
 
 1.1950 
 
 3414 
 
 .2675 
 
 3621 
 
 1.6465 
 
 4703 
 
 2.0730 
 
 5923 
 
 400 
 
 1 2570 
 
 3142 
 
 .3290 
 
 3322 
 
 1.7060 
 
 4265 
 
 2.1325 
 
 5331 
 
 450 
 
 1.3230 
 
 2940 
 
 .3940 
 
 3098 
 
 1.7665 
 
 3924 
 
 2.1940 
 
 4875 
 
 500 
 
 1.3900 
 
 2780 
 
 .4590 
 
 2918 
 
 1.8275 
 
 3655 
 
 2.2570 
 
 4514 
 
 550 
 
 1.4585 
 
 2652 
 
 .5265 
 
 2775 
 
 1.8900 
 
 3436 
 
 2.3200 
 
 4218 
 
 600 
 
 1.5260 
 
 2543 
 
 .5945 
 
 2657 
 
 1 9545 
 
 3258 
 
 2.3840 
 
 3973 
 
 650 
 
 1.5935 
 
 2452 
 
 .6615 
 
 2556 
 
 2.0200 
 
 3108 
 
 2.4485 
 
 3613 
 
 700 
 
 1.6615 
 
 2374 
 
 .7290 
 
 2470 
 
 .0865 
 
 2980 
 
 2.5125 
 
 3589 
 
 750 
 
 1.7300 
 
 2307 
 
 .7975 
 
 2397 
 
 2.1535 
 
 2871 - 
 
 2.5765 
 
 3435 
 
 800 
 
 1.7980 
 
 2247 
 
 1.8655 
 
 2332 
 
 2.2200 
 
 2775 
 
 2.6400 
 
 3300 
 
 850 
 
 1.8660 
 
 2195 
 
 1.9330 
 
 22,74 
 
 2.2865 
 
 2690 
 
 2.7060 
 
 3184 
 
 900 
 
 1.9340 
 
 2149 
 
 2.0015 
 
 2224 
 
 2.3540 
 
 2616 
 
 2.7715 
 
 3079 
 
 950 
 
 2.0015 
 
 2107 
 
 2.0690 
 
 2178 
 
 2.4230 
 
 2550 
 
 2.8380 
 
 2987 
 
 1000 
 
 2.0685 
 
 2068 
 
 2.1360 
 
 2136 
 
 
 
 
 
 
 
 
 
 TABLE 10. AIR 
 
 P 
 
 C. 
 
 15.70 C. 
 
 99.40 C. 
 
 200. 4 C. 
 
 PV 
 
 FXIO 
 
 PV 
 
 Fxio 
 
 PV 
 
 FX106 
 
 PV 
 
 FX106 
 
 Aim. 
 
 
 
 
 
 
 
 
 
 1 
 
 1.0000 
 
 10 6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 100 
 
 .9730 
 
 9730 
 
 1.0460 
 
 10460 
 
 1.4030 
 
 14030 
 
 
 
 
 
 150 
 
 .9840 
 
 6560 
 
 .0580 
 
 7053 
 
 1.4310 
 
 9540 
 
 1.8430 
 
 12290 
 
 200 
 
 1.0100 
 
 5050 
 
 .0855 
 
 5427 
 
 .4670 
 
 7335 
 
 1.8860 
 
 9430 
 
 250 
 
 1.0490 
 
 4196 
 
 .1260 
 
 4504 
 
 .5110 
 
 6044 
 
 1.9340 
 
 7736 
 
 300 
 
 1.0975 
 
 3658 
 
 .1740 
 
 3913 
 
 .5585 
 
 5195 
 
 1.9865 
 
 6622 
 
 350 
 
 1.1540 
 
 3297 
 
 .2250 
 
 3500 
 
 .6085 
 
 4596 
 
 2.0410 
 
 5831 
 
 400 
 
 1.2145 
 
 3036 
 
 .2835 
 
 3209 
 
 .6625 
 
 4156 
 
 20960 
 
 5240 
 
 450 
 
 1.2765 
 
 2837 
 
 .3460 
 
 2991 
 
 .7200 
 
 3822 
 
 2.1530 
 
 4785 
 
 500 
 
 1.3400 
 
 2680 
 
 1.4110 
 
 2822 
 
 .7815 
 
 3563 
 
 2.2110 
 
 4422 
 
 550 
 
 1.4040 
 
 2553 
 
 1.4740 
 
 2680 
 
 1.8440 
 
 3353 
 
 2.2700 
 
 4127 
 
 600 
 
 14700 
 
 2450 
 
 1.5375 
 
 2563 
 
 1.9060 
 
 3177 
 
 2.3300 
 
 3883 
 
 650 
 
 1.5365 
 
 2363 
 
 1.6015 
 
 2464 
 
 1.9670 
 
 3026 
 
 2.3900 
 
 3677 
 
 700 
 
 1.6020 
 
 2288 
 
 1.6670 
 
 2381 
 
 2.0300 
 
 2900 
 
 2.4515 
 
 3502 
 
 750 
 
 1.6690 
 
 2225 
 
 1.7340 
 
 2312 
 
 2.0930 
 
 2790 
 
 2.5130 
 
 3351 
 
 800 
 
 1.7345 
 
 2168 
 
 1.8000 
 
 2250 
 
 2.1555 
 
 2694 
 
 2.5750 
 
 3219 
 
 850 
 
 1.7990 
 
 2116 
 
 1.8655 
 
 2194 
 
 2.2180 
 
 2609 
 
 2.6370 
 
 3102 
 
 900 
 
 1.8640 
 
 2071 
 
 1.9300 
 
 2144 
 
 2.2830 
 
 2537 
 
 2.7000 
 
 3000 
 
 950 
 
 1.9280 
 
 2030 
 
 1.9960 
 
 2101 
 
 2.3490 
 
 2473 
 
 2.7640 
 
 2903 
 
 1000 
 
 1.9920 
 
 1992 
 
 2.0600 
 
 2060 
 
 2.4150 
 
 2415 
 
 2.8280 
 
 2828 
 
 82 
 
THE LAWS OF GASES 
 
 I shall insert here also certain supplementary results obtained 
 from these curves, which will be found useful in correcting the 
 readings of gas manometers. To these I append the results of 
 experiments made in 1864 at Fourvieres with the same end in 
 view : 
 
 TABLE 10 (2). VOLUMES 
 (Same Unit of Mass as Heretofore) 
 
 p 
 
 OXYGEN AT 
 15.65 0. 
 
 FxlO 6 
 
 H YDROGEN AT 
 15.50 C. 
 
 FxlO 6 
 
 NITROGEN AT 
 16 05 C. 
 
 FxlO 6 
 
 AIR AT 
 
 15.70 C. 
 FxlO 6 
 
 125 Aim. 
 175 " 
 225 " 
 275 " 
 325 " 
 375 " 
 425 " 
 475 " 
 
 7976 
 ' 5663 
 4456 
 3735 
 3261 
 2939 
 2706 
 2528 
 
 9168 
 6746 
 5411 
 4552 
 3959 
 3528 
 3199 
 2940 
 
 8560 
 6255 
 5044 
 4298 
 3790 
 3460 
 3205 
 3003 
 
 8400 
 6114 
 4907 
 4178 
 3689 
 3343 
 3094 
 2900 
 
 TABLE 11. EXPERIMENTS AT FOURVIERES 
 
 (Values of PV at \) 
 
 PRESSURES IN 
 METERS 
 
 ,76 
 
 20 
 25 
 30 
 35 
 40 
 45 
 50 
 55 
 60 
 65 
 
 NITROGEN 
 
 AIR 
 
 1.0000 
 
 1.0000 
 
 .9930 
 
 .9901 
 
 .9919 
 
 .9876 
 
 .9908 
 
 .9855 
 
 .9899 
 
 .9832 
 
 .9896 
 
 .9824 
 
 .9895 
 
 .9815 
 
 .9897 
 
 .9808 
 
 .9902 
 
 .9804 
 
 .9908 
 
 .9803 
 
 .9913 
 
 .9807 
 
 83 
 
MEMOIRS ON 
 
 TABLE 12. DATA FOR THE COMPUTATION OF THE COEFFI- 
 CIENTS OF PRESSURE 
 
 (Pressure at Constant Volume) 
 
 CONSTANT 
 
 OXYGKN 
 
 CONSTANT 
 
 HYDROGEN 
 
 VOLUME 
 
 0C. 
 
 16.65C. 
 
 99.50C. 
 
 199. 50 C. 
 
 VOLUME 
 
 C. 
 
 15.5C. 
 
 99.25C. 
 
 2(;0.2CC. 
 
 rxio 6 
 
 Atm. 
 
 Atm. 
 
 Atm. 
 
 Atm. 
 
 FX10 
 
 Aim. 
 
 Atm. 
 
 Atm. 
 
 Atm. 
 
 9205 
 
 100 
 
 108 
 
 149 
 
 196 
 
 10690 
 
 100 
 
 106 
 
 137 
 
 174 
 
 6090 
 
 150 
 
 163 
 
 233 
 
 312 
 
 7353 
 
 150 
 
 159 
 
 207 
 
 262 
 
 4570 
 
 200 
 
 219 
 
 322 
 
 437 
 
 5690 
 
 200 
 
 212 
 
 276 
 
 351 
 
 3726 
 
 250 
 
 276 
 
 415 
 
 566 
 
 4692 
 
 250 
 
 265 
 
 345 
 
 439 
 
 3208 
 
 300 
 
 332 
 
 508 
 
 698 
 
 4030 
 
 300 
 
 318 
 
 414 
 
 528 
 
 2869 
 
 350 
 
 388 
 
 598 
 
 827 
 
 3560 
 
 350 
 
 370 
 
 482 
 
 614 
 
 2629 
 
 400 
 
 446 
 
 691 
 
 
 
 3207 
 
 400 
 
 423 
 
 551 
 
 700 
 
 2450 
 
 450 
 
 502 
 
 781 
 
 
 
 2933 
 
 450 
 
 476 
 
 620 
 
 788 
 
 2312 
 
 500 
 
 558 
 
 868 
 
 
 
 2713 
 
 500 
 
 530 
 
 688 
 
 874 
 
 2204 
 
 550 
 
 624 
 
 953 
 
 
 
 2533 
 
 550 
 
 582 
 
 756 
 
 
 
 
 
 
 
 
 2386 
 
 600 
 
 635 
 
 824 
 
 
 
 
 
 
 
 
 2259 
 
 650 
 
 687 
 
 891 
 
 
 
 
 
 
 
 
 , 2149 
 
 700 
 
 741 
 
 960 
 
 
 
 CONSTANT 
 VOLUME 
 
 NITROGEN 
 
 CONSTANT 
 VOLUME 
 
 AIR 
 
 0C. 
 
 16.03C. 
 
 99.4. r >oc. 
 
 199.5 C. 
 
 oc. 
 
 15.70C. 
 
 99.40C. 
 
 200.40 C. 
 
 FX106 
 
 Atm. 
 
 Atm. 
 
 Atm, 
 
 Atm. 
 
 FX10 
 
 Atm. 
 
 Atm. 
 
 Atm. 
 
 Atm. 
 
 9910 
 
 100 
 
 107 
 
 146 
 
 192 
 
 9730 
 
 100 
 
 107 
 
 146 
 
 193 
 
 6723 
 
 150 
 
 162 
 
 225 
 
 299 
 
 6560 
 
 150 
 
 162 
 
 227 
 
 303 
 
 5195 
 
 200 
 
 217 
 
 307 
 
 414 
 
 5050 
 
 200 
 
 217 
 
 310 
 
 420 
 
 4330 
 
 250 
 
 273 
 
 392 
 
 530 
 
 4196 
 
 250 
 
 373 
 
 395 
 
 538 
 
 3786 
 
 300 
 
 328 
 
 474 
 
 644 
 
 3658 
 
 300 
 
 329 
 
 479 
 
 655 
 
 3414 
 
 350 
 
 383 
 
 556 
 
 758 
 
 3297 
 
 350 
 
 383 
 
 564 
 
 770 
 
 3142 
 
 400 
 
 439 
 
 637 
 
 869 
 
 3036 
 
 400 
 
 439 
 
 646 
 
 881 
 
 2940 
 
 450 
 
 494 
 
 718 
 
 
 
 2837 
 
 450 
 
 495 
 
 728 
 
 993 
 
 2780 
 
 500 
 
 548 
 
 797 
 
 
 2680 
 
 500 
 
 550 
 
 807 
 
 
 
 2652 
 
 550 
 
 602 
 
 875 
 
 
 2553 
 
 550 
 
 603 
 
 887 
 
 
 
 2543 
 
 690 
 
 656 
 
 957 
 
 
 2450 
 
 600 
 
 658 
 
 970 
 
 
 
 The following tables relative to carbon dioxide and ethylene 
 contain the .valueSxOi .the products P V only : 
 
THE LAWS OF GASES 
 
 TABLE 13. VALUES OF PV FOR CARBON DIOXIDE 
 
 p 
 
 oc. 
 
 10 C. 
 
 20 C. 
 
 30 C. 
 
 40 C. 
 
 50 C. 
 
 60 C. 
 
 Atm. 
 
 
 
 
 
 
 
 
 1 
 
 1.0000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 50 
 
 .1050 
 
 .1145 
 
 .6800 
 
 .7750 
 
 .8500 
 
 .9200 
 
 .9840 
 
 75 
 
 .1530 
 
 .1630 
 
 .1800 
 
 .2190 
 
 .6200 
 
 .7470 
 
 .8410 
 
 100 
 
 .2020 
 
 .2130 
 
 .2285 
 
 .2550 
 
 .3090 
 
 .4910 
 
 .6610 
 
 125 
 
 .2490 
 
 .2620 
 
 .2785 
 
 .3000 
 
 .3350 
 
 .3950 
 
 .5100 
 
 150 
 
 .2950 
 
 .3090 
 
 .3260 
 
 .3460 
 
 .3770 
 
 .4190 
 
 .4850 
 
 175 
 
 .3405 
 
 .3550 
 
 .3725 
 
 .3930 
 
 .4215 
 
 .4570 
 
 .5055 
 
 200 
 
 .3850 
 
 .4010 
 
 .4190 
 
 .4400 
 
 .4675 
 
 .5000 
 
 .5425 
 
 225 
 
 .4305 
 
 .4455 
 
 .4655 
 
 .4875 
 
 .5130 
 
 .5425 
 
 .5825 
 
 250 
 
 .4740 
 
 .4900 
 
 .5100 
 
 .5335 
 
 .5580 
 
 .5865 
 
 .6250 
 
 275 
 
 .5170 
 
 .5340 
 
 .5545 
 
 .5775 
 
 .6040 
 
 .6330 
 
 .6675 
 
 300 
 
 .5595 
 
 .5775 
 
 .5985 
 
 .6225 
 
 .6485 
 
 .6765 
 
 .7100 
 
 350 
 
 .6445 
 
 .6640 
 
 .6850 
 
 .7090 
 
 .7365 
 
 .7650 
 
 .7980 
 
 400 
 
 .7280 
 
 .7475 
 
 .7710 
 
 .7950 
 
 .8230 
 
 .8515 
 
 .8840 
 
 450 
 
 .8090 
 
 .8310 
 
 .8550 
 
 .8800 
 
 .9075 
 
 .9365 
 
 .9690 
 
 500 
 
 .8905 
 
 .9130 
 
 .9380 
 
 .9630 
 
 .9900 
 
 1.0210 
 
 1.0540 
 
 550 
 
 .9700 
 
 .9935 
 
 1.0200 
 
 .0465 
 
 1.0740 
 
 1.1035 
 
 1.1370 
 
 600 
 
 1.0495 
 
 1.0730 
 
 1.0995 
 
 .1275 
 
 1.1570 
 
 1.1865 
 
 1.2190 
 
 650 
 
 1.1275 
 
 1.1530 
 
 1.1800 
 
 .2075 
 
 1.2375 
 
 1.2680 
 
 1.3010 
 
 700 
 
 1.2055 
 
 1.2320 
 
 1.2590 
 
 .2890 
 
 1.3190 
 
 1.3500 
 
 1.3825 
 
 750 
 
 1.2815 
 
 1.3105 
 
 1.3395 
 
 .3700 
 
 1.4000 
 
 1 4315 
 
 1.4640 
 
 800 
 
 1.3580 
 
 1.3870 
 
 1.4170 
 
 .4475 
 
 1.4790 
 
 1.5105 
 
 1.5435 
 
 850 
 
 1.4340 
 
 1.4625 
 
 1.4935 
 
 .5245 
 
 1.5570 
 
 1.5885 
 
 1.6225 
 
 900 
 
 1.5090 
 
 1.5385 
 
 15685 
 
 .6000 
 
 1.6325 
 
 1.6650 
 
 1.6995 
 
 950 
 
 1.5830 
 
 1.6115 
 
 1.6430 
 
 6740 
 
 1.7065 
 
 1.7395 
 
 1.7745 
 
 1000 
 
 1.6560 
 
 1.6850 
 
 1.7160 
 
 1.7480 
 
 1.7800 
 
 1.8140 
 
 1.8475 
 
 r 
 
 70 C. 
 
 80 C. 
 
 90 C. 
 
 ]00C. 
 
 137 C. 
 
 198 C. 
 
 258 C. 
 
 Atm. 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 50 
 
 1.0430 
 
 1.0960 
 
 1.1530 
 
 1 2065 
 
 1.3800 
 
 
 
 _ 
 
 75 
 
 .9180 
 
 .9880 
 
 1.0515 
 
 1.1180 
 
 1.3185 
 
 1.6150 
 
 1.8670 
 
 100 
 
 .7770 
 
 .8725 
 
 .9535 
 
 1.0300 
 
 1.2590 
 
 15820 
 
 1.8470 
 
 125 
 
 .6430 
 
 .7590 
 
 .8580 
 
 .9470 
 
 1.2050 
 
 1.5530 
 
 1.8310 
 
 150 
 
 .5750 
 
 .6805 
 
 .7815 
 
 .8780 
 
 1.1585 
 
 1.5295 
 
 1.8180 
 
 175 
 
 .5730 
 
 .6515 
 
 .7410 
 
 .8320 
 
 1.1230 
 
 1.5100 
 
 1.8095 
 
 200 
 
 .5955 
 
 .6600 
 
 .7315 
 
 .8145 
 
 1.0960 
 
 1.4960 
 
 1.8040 
 
 225 
 
 .6285 
 
 .6815 
 
 .7460 
 
 .8175 
 
 1.0835 
 
 1.4890 
 
 1.8035 
 
 250 
 
 .6670 
 
 .7135 
 
 .7690 
 
 .8355 
 
 1.0810 
 
 1.4870 
 
 1.8060 
 
 275 
 
 .7070 
 
 .7515 
 
 .8015 
 
 .8600 
 
 1.0885 
 
 1.4875 
 
 1.8115 
 
 300 
 
 .7485 
 
 .7900 
 
 ,8375 
 
 .8900 
 
 1.1080 
 
 1.4935 
 
 1.8200 
 
 350 
 
 .8325 
 
 .8725 
 
 .9135 
 
 .9615 
 
 1.1565 
 
 1.5210 
 
 1.8465 
 
 400 
 
 .9180 
 
 .9560 
 
 .9660 
 
 1.0385 
 
 1.2175 
 
 1.5630 
 
 1.8830 
 
 450 
 
 1.0035 
 
 1.0400 
 
 1.0775 
 
 1.1190 
 
 1.2880 
 
 1.6160 
 
 1.9280 
 
 500 
 
 1.0880 
 
 1.1240 
 
 1.1610 
 
 1.2005 
 
 1.3620 
 
 1.6775 
 
 
 
 550 
 
 1.1720 
 
 1.2085 
 
 1.2430 
 
 1.2830 
 
 1.4400 
 
 1.7450 
 
 
 
 600 
 
 1.2540 
 
 1.2900 
 
 1.3265 
 
 1.3655 
 
 1.5180 
 
 ' 1.8120 
 
 
 
 650 
 
 1.3360 
 
 1.3725 
 
 1.4085 
 
 1.4475 
 
 1.5960 
 
 1.8835 
 
 
 
 700 
 
 1.4170 
 
 1.4535 
 
 1.4900 
 
 1.5285 
 
 1.6760 
 
 1.9560 
 
 
 
 750 
 
 1.4985 
 
 1.5335 
 
 1.5705 
 
 1.6100 
 
 1.7565 
 
 2.0330 
 
 
 
 800 
 
 1.5780 
 
 1.6140 
 
 1.6505 
 
 1.6890 
 
 1.8355 
 
 21080 
 
 
 
 850 
 
 1.6575 
 
 1.6925 
 
 1.7285 
 
 1.7680 
 
 1 9150 
 
 21860 
 
 
 
 900 
 
 1.7345 
 
 1.7710 
 
 1.8075 
 
 1.8460 
 
 1.9940 
 
 2.2600 
 
 
 
 950 
 
 1.8100 
 
 1 8470 
 
 1.8845 
 
 1.9230 
 
 2.0720 
 
 2.8350 
 
 
 
 1000 
 
 1.8840 
 
 1.9210 
 
 1.9590 
 
 1.9990 
 
 
 
 
 
 
 
 85 
 
MEMOIRS ON 
 
 Atm. 
 
 31 
 
 33 
 
 34 
 
 35 
 37 
 
 40 
 
 44 
 
 45 
 
 48 
 
 50 
 
 53 
 
 55 
 
 56 
 
 57 
 
 60 
 
 65 
 
 68 
 
 70 
 
 71 
 
 72 
 
 73 
 
 74 
 
 75" 
 
 78 
 80 
 
 85 
 
 95 
 100 
 110 
 
 TABLE 14. CARBON DIOXIDE 
 
 (Supplementary Table for Values of PV) 
 
 
 
 100 
 
 200 
 
 30 
 
 32 
 
 350 
 
 400 
 
 50 
 
 600 
 
 700 
 
 80 
 
 90 
 
 1000 
 
 .7380 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7 1 on 
 
 7860 
 
 
 
 
 
 
 
 
 
 
 
 
 . f IzU 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 6990 
 .0750 
 
 ^7640 
 
 .8350 
 
 
 
 
 
 
 
 
 
 _ 
 
 
 
 
 
 
 
 
 
 
 
 .0790 
 
 .7420 
 
 .8170 
 
 .8820 
 
 
 
 
 
 __ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .7060 
 
 .7895 
 
 .8590 
 
 .8750 
 
 .8920 
 
 .9235 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .6530 
 
 .7490 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .1050 
 
 .7380 
 
 .8190 
 
 .8350 
 
 .8555 
 
 .8880 
 
 .9520 
 
 1.0110 
 
 1.0660 
 
 
 
 
 
 
 
 
 
 
 .7060 
 
 .7930 
 
 
 
 
 
 .8670 
 
 .9330 
 
 .9950 
 
 1.0520 
 
 
 
 
 
 
 
 1.1050 
 
 .1145 
 
 .6800 
 
 .7750 
 
 .7920 
 
 .8155 
 
 .8525 
 
 .9210 
 
 .9840 
 
 1.0430 
 
 1.0980 
 
 1.1535 
 
 1.2070 
 
 
 
 .6370 
 
 .7460 
 
 
 
 
 
 .8300 
 
 .9020 
 
 .9680 
 
 1.0280 
 
 1.0850 
 
 1.1420 
 
 1.1960 
 
 
 
 
 
 .6050 
 
 .7260 
 
 .7455 
 
 .7720 
 
 .8135 
 
 .8890 
 
 .9570 
 
 1.0185 
 
 1.0760 
 
 1.1340 
 
 1.1785 
 
 
 
 
 
 .5850 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .1480 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .1520 
 
 .6680 
 
 .6935 
 
 .7245 
 
 .7720 
 
 .8555 
 
 .9285 
 
 .9940 
 
 1.0540 
 
 1.1130 
 
 1.1710 
 
 
 
 
 
 
 .5950 
 
 .6290 
 
 .6690 
 
 .7260 
 
 .8200 
 
 .8990 
 
 .9690 
 
 1.0325 
 
 1.0930 
 
 1.1530 
 
 
 
 
 
 
 
 .5350 
 
 .5780 
 
 .6310 
 
 .6950 
 
 .7970 
 
 .8810 
 
 .9530 
 
 1.0190 
 
 1.0810 
 
 1.1420 
 
 
 
 
 
 
 
 .4700 
 2300 
 
 .5400 
 
 .6020 
 
 .6730 
 
 .7820 
 
 .8685 
 
 .9430 
 
 1.0100 
 
 1.0730 
 
 1.1350 
 
 ~ 
 
 _ 
 
 
 
 .2230 
 
 .4910 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .4600 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .2190 
 
 .4050 
 
 .5310 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _ 
 
 _ 
 
 .2190 
 
 .2680 
 
 .5100 
 
 .6130 
 
 .7410 
 
 .8360 
 
 .9170 
 
 .9880 
 
 1.0535 
 
 1.1180 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _ 
 
 
 .2205 
 
 .2410 
 
 .4200 
 
 
 
 
 
 _ 
 
 
 
 _ 
 
 _ 
 
 _ 
 
 
 
 
 
 
 
 .2225 
 
 
 
 .3180 
 
 .5400 
 
 .7000 
 
 .8030 
 
 .8900 
 
 .9660 
 
 1.0335 
 
 1.1005 
 
 
 
 
 
 
 2810 
 
 5030 
 
 
 
 
 
 
 
 
 _ 
 
 _ 
 
 _ 
 
 _ 
 
 .2670 
 
 .4350 
 
 6510 
 
 .7690 
 
 .8630 
 
 .9425 
 
 1.0135 
 
 1.0835 
 
 
 
 
 
 
 
 
 
 
 
 .2650 
 
 .3410 
 
 .5990 
 
 .7340 
 
 .8350 
 
 .9190 
 
 .9935 
 
 1.0655 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .3140 
 
 .5460 
 
 .6980 
 
 .8060 
 
 .8960 
 
 .9735 
 
 1.0480 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .3090 
 
 .4910 
 
 .6610 
 
 .7770 
 
 .8720 
 
 .9540 
 
 1.0305 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .3130 
 
 .4170 
 
 .5880 
 
 .7210 
 
 .8240 
 
 .9140 
 
 .9970 
 
 [Tor Table 15, see p. 87.] 
 
 TAI 
 P 
 
 JLE 1 
 
 
 
 6. 
 
 50 
 
 3UPP 
 
 7.50 
 
 LEMJ 
 
 10 
 
 EKT^ 
 20 
 
 LEY 
 30 
 
 VALL 
 
 40 
 
 'ES C 
 
 50 
 
 >F PI 
 
 60 
 
 7 FOI 
 
 T0 
 
 1 ET1 
 
 80 
 
 IYLE 
 
 90 
 
 NE 
 100 
 
 Atm. 
 36 
 37 
 38 
 39 
 40 
 41 
 42 
 43 
 44 
 45 
 4i> 
 47 
 48 
 49 
 50 
 51 
 52 
 53 
 54 
 56 
 58 
 60 
 65 
 70 
 75 
 80 
 90 
 100 
 
 .6340 
 .6165 
 .5955 
 
 .5330 
 .1610 
 .1570 
 .1580 
 .1600 
 
 .1645 
 .1095 
 .1755 
 .1810 
 
 .2025 
 
 .2425 
 .2565 
 
 ,3100 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .6490 
 .6155 
 
 .6735 
 .6425 
 
 .6820 
 .6685 
 
 
 
 
 
 - 
 
 - 
 
 - 
 
 
 
 
 
 
 - 
 
 .5730 
 .5470 
 .5150 
 .4770 
 .1890 
 .1850 
 . 1855 
 . 1875 
 . 1900 
 
 .1945 
 
 .2050 
 .2145 
 
 .2535 
 
 .6085 
 
 .6370 
 
 .7320 
 
 - 
 
 
 
 - 
 
 
 
 - 
 
 - 
 
 
 
 - 
 
 .5675 
 
 .5100 
 .4670 
 .3300 
 . 2150 
 .2075 
 
 .2060 
 
 .6030 
 .5620 
 
 .5075 
 .4700 
 .4200 
 .2900 
 .2400 
 
 .6980 
 .6840 
 
 .6290 
 .5975 
 
 .7310 
 
 .8300 
 .8140 
 
 .8865 
 
 - 
 
 \ 
 
 - 
 
 - 
 
 - 
 
 
 
 
 
 
 
 
 
 .2090 
 .2125 
 .5180 
 
 .2290 
 .2270 
 .2285 
 .2315 
 
 .2655 
 .2785 
 
 .3303 
 
 .5610 
 .5235 
 .4805 
 .4300 
 .3310 
 .3110 
 .3110 
 .3165 
 .3370 
 .3 GOO 
 
 .6905 
 
 .6195 
 .5500 
 .4830 
 .4300 
 .3990 
 .3915 
 .4030 
 
 .7810 
 
 .7285 
 . 6805 
 .6310 
 .5805 
 .5390 
 .4875 
 .4710 
 
 86 
 
 .8595 
 
 .8170 
 
 .7430 
 .7045 
 .6660 
 .6060 
 .5665 
 
 .9290 
 
 .8925 
 
 .8315 
 .8000 
 .7670 
 .7090 
 .6680 
 
 .9850 
 .9630 
 
 .9090 
 .8815 
 . 8555 
 .8035 
 .7620 
 
 1.0285 
 
 .9795 
 .9550 
 .9310 
 .8840 
 .8465 
 
 1.0920 
 
 1.0260 
 1.0050 
 
 .9265 
 
 1.1530 
 
 1.0940 
 1.0755 
 
 1.0050 
 
THE LAWS OF GASES 
 
 OOiOOOOiOOiOO*OO*OOiOOifci>O-<2:Oi6SO-3OTh- l ^ 
 OOOOOOOOOOOOOOOOOxOOiOOiOOtO 
 
 *a *o i& M 
 
 Oh- l l L tT> 
 
 o o co oo GO - 
 
 oo tc 
 
 <% 
 
 Or Oi O< Oi O< O( O Oi O O Ot Or Ot Or O O Ot O O Ot O Ot Or Ot 
 
 c 
 
 ^ ^ 
 
 O O Oi O 
 
 O U O( OT h- 1 O O O O O 
 
 O Ci 
 
 S^OO-^-^JOtOCGOOi^GiOr 
 ? 6 O O O O< O O O O Ot O 
 
 Ot Oi O O* O O O"? O< O O O Oi Oi O Or O 
 
 - 
 
 ^O^>CC>^C' 
 OT O Ot O O 
 
 O O 
 
 CO CO W tfi I- 4 H* Q <O GO <2 O6 Ot tf*- W CO 00 
 
 GO 
 
 o 
 
 O I ' 
 
 O O CO CO CO 00 00 00 CO O fcO Q5 rf*O3 CO rf^ Ctt 00 !-* CJi 
 
 O^OOOOOGOOGOOOOOOOCOOOOOO 
 
 87 
 
MEMOIRS ON 
 
 s 
 
 g JO O O O JO O JO 
 
 00 oi O T-! -^ so os' | | | | 
 
 lOtOCDCOOOCO-rHOlOO 
 O OS CO OT! CO r-i i-I T-( CO 
 lO 
 
 T-I rH T-I C<> CO OS 
 
 1 T-I so d | 
 
 r-i TH <M CO OO 
 
 t rJH O T-4 1 o i> 
 
 GQOJ>-OCQCOrHCOOrHCO 
 OS O O} JO JO JO JO 
 
 TH TH rH CO CO C5 
 
 SOBi 'OSOOCOCOt-OOJOOQ 
 I TH CO JO JO CO t- 00 00 OS JO t- JO 
 
 TH Tfl t^ 
 
 5 
 
 id JO -H co cd cb 
 
 i> JO <* CO <N (M rH 
 
 rH T-I GQ CO ^* 
 
 TH j> o ^* oo 
 ^ ^^^( 
 
 gCOOOCOOOO^GQOO 
 >- {> TH 10 -^ CO CD r^' JO CO 
 
 r-i^OO-^COOS'-i 
 ' TH rH GO CO JO i> 
 
 ^ 70 CO (M JO JO JO 
 O7 rH CO JO O7 00 C5 CO 
 
 ft ^ O IsjCOCOWrHQOCOOOO 
 
 S j -S od t-- ^ co o o co r-' i 
 
 H ^ pi. ^3 ^ ift 
 
 ft 
 
 H 
 
 r-' o 11 o co co oo' os 
 
 OOOOS'HCOOJOTf 
 
 OS CQ Oi rH JO CO TH rH J 
 
 '-H^rHOS 
 
 rH T 1 CO CO 
 
 
 ~ O C7 (75 00 CQ O (M W *O 
 
 to o co c-i o co o 
 
THE LAWS OF GASES 
 
 EXAMINATION OF THE KESULTS 
 
 General Laws 
 
 An inspection of the above results will lead to inferences 
 similar in a general way to those which I adduced in my 
 memoir of 1881. I shall now, moreover, be able to examine a 
 
 2.00 
 1.90 
 1.80 
 1.70 
 1.60 
 1.50 
 1.40 
 1.30 
 1.20 
 1.10 
 1.00 
 0.90 
 0.80 
 0.70 
 0.60 
 0.50 
 0.40 
 0.30 
 0.20 
 0.10 
 
 Atm. P.100 
 
 200 
 
 300 
 
 400 500 600 
 
 FIG. 9. 
 
 700 
 
 800 
 
 900 
 
 1000 
 
 great number of moot points, relative to which no decision 
 could certainly have been made by aid of investigations no 
 more extensive than those heretofore available. 
 
 It did not seem necessary to give all the curves for the divers 
 
MEMOIRS ON 
 
 gases, seeing that the principal types were drawn in full in my 
 first research. The group of isotherms for carbon dioxide 
 graphically represented within the limits actually reached suf- 
 fice for exhibiting the results in their general features. The 
 first diagram (Fig. 9) shows the isotherms for this gas, when 
 the pressures are laid off as abscissas and the products PFas 
 ordinates. The second diagram (Fig. 10) shows the region in 
 
 2.00 1 
 
 T.75 _ 
 
 1.50 
 
 1.25 
 
 J.OO 
 
 0.75 
 
 0.50 - 
 
 0.25 
 
 Atm. P. 25 
 
 250 
 
 the neighborhood of the critical point with more detail. The 
 part of the isotherms represented by dotted lines has been 
 added merely to round off the figures. They have not been 
 made the subject of measurement in the present paper, except- 
 ing the lines for 32 and 35, which are dotted throughout. 
 
 At temperatures lower than the critical point, a part of the 
 isotherms is in the form of straight vertical lines, correspond- 
 ing to liquefaction. These did not occur in my first group of 
 curves, which began at 35. 
 
 The ordinates of the extremities of each straight part show 
 
 90 
 
THE LAWS OF GASES 
 
 the volume in the liquid state and the corresponding volume 
 of the saturated vapor, and hence, also, the densities of the two 
 states, respectively. The locus of these points is Andrews's 
 curve of liquefaction, and has been traced in the second dia- 
 gram (Fig. 10). Another dotted curve, recalling, as does the 
 preceding, the form of a parabola between the limits of con- 
 struction, is the locus of the points of minimum ordiriates, P V. 
 The abscissas of this curve pass through a maximum, as was to 
 be anticipated from the facts which I have already indicated 
 elsewhere i.e., for gases in a region remote from their critical 
 points, like methane, air, nitrogen, the abscissa of the mini- 
 mum ordinate shows a retrograde march for continually in- 
 creasing temperatures, an inversion of what took place in the 
 case of carbon dioxide within the field to which I was then re- 
 stricted. The following table gives the maximum vapor ten- 
 sion, the pressure corresponding to the minimum ordinates at 
 the different temperatures, as well as the value of PFat that 
 ordinate for the gases oxygen, carbon dioxide, and ethyl ene : 
 
 TABLE 19 
 
 VALUES OF PV 
 
 VAPOR 
 TENSION 
 
 T 
 
 CARBON DIOXIDE 
 
 ETHYLENE 
 
 OXYGEN 
 
 CARB. 
 DIOX 
 
 ETHY- 
 LENE 
 
 P 
 
 PV 
 
 P 
 
 PV 
 
 P 
 
 PV 
 
 P 
 
 P 
 
 ~"c~ 
 
 Aim. 
 
 
 Aim. 
 
 
 Aim. 
 
 
 Aim. 
 
 Aim. 
 
 
 
 34.5 
 
 .0740 
 
 42 
 
 .1570 
 
 175 
 
 .9120 
 
 34.4 
 
 40.6 
 
 5 
 
 
 
 
 
 47.5 
 
 .1850 
 
 
 
 
 
 
 
 45.5 
 
 7.5 
 
 
 
 
 
 51.5 
 
 .2055 
 
 
 
 
 
 
 
 48.1 
 
 10 
 
 44.5 
 
 .1035 
 
 55.7 
 
 .2270 
 
 
 
 
 
 44.4 
 
 51.1 
 
 15 
 
 
 
 
 
 
 
 
 
 165 
 
 .9910 
 
 
 
 . 
 
 20 
 
 56.8 
 
 .1475 
 
 72 
 
 .3095 
 
 
 
 
 
 56.4 
 
 . 
 
 30 
 
 76 
 
 .2185 
 
 87 
 
 .3900 
 
 
 
 
 
 70.7 
 
 
 
 40 
 
 101 
 
 .3083 
 
 101 
 
 .4700 
 
 
 
 
 
 
 
 50 
 
 125 
 
 .3465 
 
 114 
 
 .5485 
 
 
 
 
 
 
 
 60 
 
 143 
 
 .4830 
 
 125 
 
 .6245 
 
 
 
 
 
 
 
 70 
 
 162 
 
 .5690 
 
 135 
 
 .7030 
 
 
 
 
 
 
 
 80 
 
 179 
 
 .6500 
 
 145 
 
 .9750 
 
 
 
 
 
 
 
 90 
 
 196 
 
 .7310 
 
 153 
 
 .8490 
 
 
 
 
 
 
 
 100 
 
 210 
 
 .8140 
 
 161 
 
 .9220 
 
 100 
 
 1.3750 
 
 
 
 137 
 
 245 
 
 1.0850 
 
 185 
 
 1.1660 
 
 
 
 
 
 
 
 198 
 
 255 
 
 1.4920 
 
 188 
 
 1.5340 
 
 
 
 
 
 
 
 258 
 
 218 
 
 1.8100 
 
 
 
 
 
 
 
 
 
 
 =====- 
 
 91 
 
 / OK THK ^J" 
 
MEMOIRS ON 
 
 The temperature 10 C., corresponding to the maximum 
 vapor pressure 51 atmospheres, appears from the form of the 
 isotherms for ethylene to be extremely near the critical tem- 
 perature. These results are thus approximately identical 
 with the data obtained by Mr. J. Dewar. The method pur- 
 sued does not admit of a direct determination of the point 
 in question, and critical data can be deduced from the table 
 only by calculation based on the intrinsic equation of the 
 gas. 
 
 Quite recently M. Mitkowski,* in an interesting paper on 
 the compressibility of air, has prolonged the locus of mini- 
 mum ordinates as far as 145 C., and has shown that this 
 gas has a maximum abscissa at about 75 C. and 124 atmos- 
 pheres. 
 
 The form of the isotherms beyond the region of minimum 
 ordinates is one of the questions which I particularly wished to 
 investigate. These curves, beginning with a distance from the 
 ordinates in question, which is smaller in proportion as the tem- 
 perature is lower, seemed to me to undergo a transformation 
 into lines sensibly straight. I was aware of the existence of 
 slight curvature ; but this was so little marked as to suggest 
 that further prolongation of the family of curves would bring 
 out a fascicle of parallel straight lines more and more clearly. In 
 fact, this hypothesis proved to be specially attractive, inasmuch 
 as the angular coefficient of these fascicles severally gave the 
 limit of volume for an infinite pressure. Hence they lead to 
 a very simple interpretation of the covolutne, thus found direct- 
 ly and with precision. 
 
 Unfortunately, this hypothesis of mine does not seem to be 
 verified at least, within the limits of temperature and pressure 
 of the present research. The isotherms all present a concavity 
 towards the abscissa, slight, it is true, but nevertheless beyond 
 question. Concavity is expressible as a diminution of the an- 
 gular coefficient of the tangent, and I have summarized the 
 
 P' V'PV 
 
 values of the coefficient - , =e in the following tn- 
 
 f mT 
 
 ble. This gives t between the pressure limits given in the 
 first column at the different temperatures indicated in the 
 first row. 
 
 * Academie des Sciences de Cracovie, 1891. 
 92 
 
THE LAWS OF GASES 
 
 p'V' PV 
 
 TABLE 20. VALUES OF e = p ,_ p 
 
 
 HYDROGEX 
 X 106 AT 
 
 NITROGKN 
 6 X 106 AT 
 
 AIR 
 e X 106 AT 
 
 OXYGEN 
 6 X 106 AT 
 
 oc. 
 
 47.3 
 
 0C. 
 
 43.6 
 
 0C. 
 
 45.1 
 
 0C. 
 
 Aim. Aim. 
 
 From 500 to 1000. 
 " 1000 " 1500. 
 " 1500 " 2000. 
 " 2000 " 2500. 
 " 2500 " 8000. 
 
 732 
 
 690 
 638 
 612 
 579 
 
 693 
 643 
 
 618 
 
 588 
 
 1300 
 1213 
 1186 
 1154 
 
 1316 
 1233 
 1176 
 1168 
 
 1264 
 1190 
 1301 
 1063 
 
 1261 
 1206 
 1147 
 1090 
 
 1158 
 1106 
 1054 
 1015 
 971 
 
 
 
 HYDROGKN 
 t X 106 AT 
 
 ETHYLRXK 
 e X 10 6 AT 
 
 CARBOX DIOXIDE 
 
 e X 106 AT 
 
 C. 
 
 99. '25 
 
 200.5 
 
 oc. 
 
 1000 
 
 0C. 
 
 100.00 
 
 Atm. Aim. 
 
 From 200 to 400 
 
 725 
 742 
 730 
 712 
 
 727 
 725 
 725 
 720 
 
 730 
 732 
 719 
 
 _ 
 
 2357 
 
 2180 
 2080 
 2002 
 
 2195 
 
 2157 
 2090 
 
 1715 
 
 Ki07 
 1542 
 1490 
 
 1635 
 1617 
 1550 
 
 " 400 " 600 
 " 600 " 800 
 " 800 " 1000.. 
 
 Clearly the isotherms present slight curvature, as pointed out 
 above. Between the same pressure limits the angular coeffi- 
 cient increases by a small amount with temperature. This in- 
 crement corresponds to widening of the fascicle, which is dis- 
 tinctly seen for the case of carbon dioxide in the region of 
 lower temperatures. As temperature increases the curves grad- 
 ually cease to spread apart. In the permanent gases like 
 hydrogen, nitrogen, and air the variation with temperature is 
 scarcely perceptible. 
 
 A comparison of the decrements of these coefficients between 
 the same pressure limits but at different temperatures shows 
 no variation clearly enough indicated to be specified like the 
 preceding; those groups of observations which extend over a 
 sufficient interval of temperature are restricted to a pressure 
 interval of 1000 atmospheres. Whether under sufficiently high 
 pressures and at high enough temperatures the angular coeffi- 
 cient will reach a limiting value cannot, therefore, be foreseen. 
 In all cases the smallest values of these coefficients are superior 
 limits of the smallest volumes possible. It might be interest- 
 ing to compare these values with those computed by aid of the 
 intrinsic equations. To take the simplest form of equation, 
 that of Van der Waals, the third part of the critical volume is 
 evidently a limit of this reduction. 
 
MEMOIRS ON 
 
 Carbon dioxide, for instance, has a critical volume of .004224, 
 the third of which, .001408, is markedly less than the smallest 
 angular coefficient, .00149. 
 
 COEFFICIENTS OF EXPANSION AT CONSTANT PRESSURE 
 
 /I dv\ 
 
 \v dt) 
 
 The laws of expansion are particularly involved in the neigh- 
 borhood of the critical point. For temperatures below the 
 critical point the coefficients can obviously not be computed 
 for pressures intermediate between the tension maxima corre- 
 sponding to the given limits of temperature; for the change of 
 volume here originates not merely in thermal expansion between 
 these states, but is due also to a change of state. In other 
 words, the coefficients are infinite between these limits, and in 
 the following table crosses are put in the place of the two co- 
 efficients which, for the reason given, are without meaning. 
 
 For pressures equal to the maximum vapor tensions at one 
 of the limits of the temperature interval, the coefficient re- 
 fers to the gaseous state for the case of the lower limit, and 
 to the liquid state for the case of the upper limit. Hence, for 
 a given temperature and at the corresponding maximum vapor 
 tension, there are two coefficients, belonging, respectively, to 
 the two states of aggregation. One refers to incipient satura- 
 tion, the other to an absence of vapor. It would be extremely 
 interesting to compare the values of these two coefficients at 
 different temperatures. Such an inquiry, however, would re- 
 quire special investigations, and on the whole present serious 
 difficulties. Since the variation of the coefficient with tem- 
 perature is very rapid under these conditions, it would be 
 necessary to greatly restrict the temperature interval on ap- 
 proaching saturation. 
 
 Two tables follow relative to carbon dioxide and ethylene 
 respectively, in which the mean coefficients of expansion are 
 given for the pressures inserted in the first vertical column. 
 The temperature intervals for which the coefficients apply are 
 shown in the first horizontal row. To avoid misapprehension, 
 it is to be observed that the coefficients are reduced or referred 
 to unit of volume by successively dividing by the volume cor- 
 responding to the lower temperature limit, and not by the 
 initial volume at zero centigrade. 
 
 94 
 

 
 THE LAWS OF GASES 
 
 CDOO 5OiOi4^O06565> k| k| 'I 'I k fcfc. 
 
 OOOOO'OOfO-3Of65h-*OCDCDOOOO-3OiCN5- 
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 OOCO OO OO OO OO 1 
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 1 1 *s 1 1 x 
 
 1 Oi 1 1 H- 
 
 
 
 95 
 
MEMOIRS ON 
 
 O G9 *> 00 OO ^ ?> 
 
 T-< CO 00 CO 
 X CO CO T* 
 
 8 
 
 O T ! O GO ^ iO 
 
 X "* O CO ?> C-.-0 CO LO ^^ ^ 
 
 e i"^ J " " ' 
 
 O 3^ CO 
 
 *-" O ^> 
 
 O5 CO O C^ * 
 
 OO CO O 
 O 00 T I 
 
 - 
 
 I \ \S *- ~ 
 
 o> X O O 
 
 ^H 
 
 T-H t- <Q CO X J> 
 
 
 e * ? S 
 
 T ( *> CO O Th CO ^t ?t ^ 7^ 
 
 O 
 
 7^ SS'O 
 
 X - 
 
 p'-t J COOOOCC5O7<?i(O^H'-f?>'?>?>'r^Ci 
 O^OOOi.O^-^HCOCO7^7^7<?7^Tlr-lrHT-H 
 
 O^JO-^COCOCOT^-TyTVT-HT^iT-H^-HT-iT i 
 
 C- C^ >0 > >C iC 
 
THE LAWS OF GASES 
 
 VARIATION OF THE COEFFICIENT OF EXPANSION WITH 
 PRESSURE 
 
 An inspection of Table 21 shows that at the outset the coeffi- 
 cient of expansion changes with pressure, in the manner al- 
 ready specified by Regna-ult for pressures of a few atmospheres. 
 It then passes through a maximum, which occurs at a pressure 
 regularly increasing with temperature. The maxima in each 
 vertical column of the tables are put in parentheses. During 
 my first researches on this subject I believed that these maxima 
 occur at the same pressure for which the product P V is a 
 minimum ; but the more extended data of the present memoir 
 show this law to be only approximate. 
 
 At the critical temperature the maximum coefficient of ex- 
 pansion evidently coincides with the critical pressure, since the 
 former is then infinite. Under other conditions, depending on 
 the form of the isotherm, this pressure is much smaller than 
 the pressure corresponding to the minimum ordinate. The 
 locus of maximum coefficients of expansion thus starts out from 
 the critical point (in my first memoir the initial isotherm was 
 taken at 35.1 C.); and since this is a point of double inflection, 
 the inquiry is pertinent whether the locus in question is not 
 identical with the point of inflection of the isotherms. This is 
 not the case. For increasing temperature, the maximum co- 
 efficient is always encountered a little earlier than the mini- 
 mum ordinate. It is thus comprehended between the locus of 
 the summits of these ordinates and the locus of the points of 
 inflection. Little by little it approaches the former, and ends 
 by intersecting it in the region of its minimum abscissa. 
 
 Table 22 for ethylene leads to a series of results of an analo- 
 gous character throughout. 
 
 The following table (23) shows for oxygen, hydrogen, nitro- 
 gen, and air that the diminution of the coefficient of expansion 
 continues regularly even as far as 3000 atmospheres. The same 
 fact is exhibited in Table 24 for the same gases throughout 
 higher temperatures. 
 
MEMOIRS ON 
 
 1 Ay 
 TABLE 23. VALUES OF - 
 
 p 
 
 OXYGEN 
 
 HYDROGEN 
 
 ^mospheres 
 
 15.6 
 
 0015.40 
 
 9047.30 
 
 1000 
 
 .00236 
 
 .00200 
 
 .00206 
 
 1500 
 
 189 
 
 178 
 
 173 
 
 2000 
 
 164 
 
 152 
 
 152 
 
 2500 
 
 147 
 
 138 
 
 137 
 
 3000 
 
 134 
 
 128 
 
 129 
 
 P 
 
 NITROGEN 
 
 AlR 
 
 Atmospheres 
 
 16.0 
 
 Oc_46.6 
 
 0015.70 
 
 0045.10 
 
 1000 
 
 .00193 
 
 .00191 
 
 .00206 
 
 .00197 
 
 1500 
 
 140 
 
 151 
 
 144 
 
 148 
 
 2000 
 
 133 
 
 131 
 
 116 
 
 126 
 
 2500 
 
 111 
 
 108 
 
 107 
 
 112 
 
 3000 
 
 098 
 
 098 
 
 110 
 
 105 
 
 VARIATION OF THE COEFFICIENT OF EXPANSION WITH 
 TEMPERATURE 
 
 The above tables, 21 and 22, show that the coefficient at first 
 increases with temperature, passes a maximum, and thereafter 
 diminishes. 
 
 Under constant pressures of successively increasing value the 
 maximum occurs at temperatures which continually increase, 
 while the maximum itself becomes less accentuated and finally 
 vanishes within the limits of the tables. An increase of value 
 alone remains, which, in its turn, gradually becomes less ap- 
 preciable. At 1000 atmospheres the maximum is certainly still 
 encountered at sufficiently high temperatures. To verify these 
 observations it suffices to treat such gases as are much farther 
 removed from their critical points. It is then manifest that 
 the maximum has been reached or even passed in all cases, as, 
 for instance, Table 24 fully evidences. All the coefficients are 
 here notably smaller between 100 and 200 than between 
 and 100. Henee the, maximum has been passed. 
 
THE LAWS OF GASES 
 
 1 A 
 TABLE 24. VALUES OF - - = a 
 
 V At 
 
 
 OXYGEN 
 
 HYDROGEN 
 
 NITROGEN 
 
 AIR 
 
 
 to 
 
 99.50 to 
 
 to 
 
 99.25 to 
 
 0to 
 
 99.45 to 
 
 to 
 
 99.4 to 
 
 
 99.5 
 
 199.5 
 
 99. 25<> 
 
 209.2 
 
 99.45 
 
 199.50 
 
 99.4 
 
 200.4 
 
 Aim. 
 
 a 
 
 
 
 a 
 
 a 
 
 a 
 
 a 
 
 a 
 
 a 
 
 100 
 
 ,00486 
 
 
 
 
 
 
 
 
 
 
 
 .00444 
 
 
 
 200 
 
 534 
 
 .00300 
 
 .00332 
 
 .00242 
 
 .00433 
 
 .00280 
 
 455 
 
 .00287 
 
 800 
 
 512 
 
 297 
 
 314 
 
 231 
 
 402 
 
 267 
 
 422 
 
 275 
 
 400 
 
 459 
 
 280 
 
 295 
 
 221 
 
 358 
 
 250 
 
 371 
 
 261 
 
 500 
 
 405 
 
 264 
 
 278 
 
 214 
 
 315 
 
 235 
 
 331 
 
 241 
 
 600 
 
 357 
 
 245 
 
 261 
 
 204 
 
 282 
 
 219 
 
 294 
 
 222 
 
 700 
 
 320 
 
 226 
 
 249 
 
 196 
 
 256 
 
 204 
 
 269 
 
 207 
 
 800 
 
 288 
 
 212 
 
 237 
 
 189 
 
 236 
 
 189 
 
 244 
 
 194 
 
 900 
 
 261 
 
 198 
 
 226 
 
 182 
 
 218 
 
 179 
 
 226 
 
 182 
 
 1000 
 
 241 
 
 
 
 218 
 
 -- 
 
 
 
 
 
 214 
 
 171 
 
 In Tables 21 and 22 the maxima relative to temperature were 
 put in square brackets. It is seen that they make up a group 
 which lies very close to the maxima relative to pressure, and 
 which, like the latter, would appear with greater regularity if 
 the limits of the temperature and the pressure intervals were 
 both narrower. The real maxima coincide, as it were, acci- 
 dentally with the numbers in the tables. 
 
 The locus of the maxima relative to temperature starts from 
 the critical point, as did the locus of the maxima relative to 
 pressure. It approaches the locus of minimum ordinates more 
 rapidly than the latter, and intersects it sooner, as it were. 
 
 Below the critical temperature the first coefficients of each 
 horizontal row in Table 21 refer to the liquid state, since the 
 pressure exceeds the maximum vapor tension. At pressures 
 lower than the critical pressure the coefficients for the gaseous 
 state, properly so called, at once decrease. As early as 1870 I 
 showed * that for the cases of carbon dioxide and sulphur di- 
 oxide the coefficients decrease regularly from C. to above 
 300 under atmospheric pressure. 
 
 For pressures of a value higher than the critical pressure 
 there is no further occasion to consider the distinction between 
 the two coefficients which I have just explained ; for the dis- 
 continuity no longer occurs under constant pressure. To ob- 
 viate all misapprehension I have marked three coefficients with 
 an asterisk (*), which, although corresponding to temperatures 
 
 * Comptes Rendus, July 4, 1870; Annales de CUimie et de Physique, 1872. 
 
 99 
 
MEMOIRS ON 
 
 below the critical temperature, belong to the gaseous state (at 
 50 and 60 atmospheres). 
 
 To return to the gaseous state : It was shown above that in 
 case of oxygen, hydrogen, nitrogen, and air the coefficient of 
 expansion has passed beyond its maximum value even at ordi- 
 nary temperatures. The following table (25*), containing values 
 
 _\ f) 
 
 of - not reduced to the unit of volume, proves that the coeffi- 
 
 cients are practically independent of temperature, oxygen alone 
 excepted : 
 
 TABLE 25*. VALUES OF - xlO 8 
 
 A t 
 
 p 
 
 OXYGEN 
 
 HYDROGEN 
 
 NITROGEN 
 
 AIR 
 
 to 
 9950 
 
 99.5 to 
 199.5 
 
 0to 
 99.25 
 
 99.25 to 
 200.2 
 
 0to 
 
 99.5 
 
 99.45 to 
 199.5 
 
 0to 
 
 99.4 
 
 99. 4 to 
 200 
 
 Atm. 
 
 
 
 
 
 
 
 
 
 100 
 
 4518 
 
 
 
 
 
 
 
 
 
 
 
 4320 
 
 
 
 200 
 
 2442 
 
 2095 
 
 1890 
 
 1835 
 
 2251 
 
 2086 
 
 2296 
 
 2095 
 
 300 
 
 1643 
 
 1440 
 
 1265 
 
 1222 
 
 1522 
 
 1414 
 
 1544 
 
 1422 
 
 400 
 
 1207 
 
 1072 
 
 947 
 
 919 
 
 1124 
 
 1066 
 
 1125 
 
 1084 
 
 500 
 
 937 
 
 856 
 
 754 
 
 741 
 
 877 
 
 859 
 
 887 
 
 859 
 
 600 
 
 756 
 
 703 
 
 624 
 
 615 
 
 718 
 
 715 
 
 720 
 
 706 
 
 700 
 
 634 
 
 592 
 
 535 
 
 526 
 
 609 
 
 609 
 
 615 
 
 602 
 
 800 
 
 541 
 
 512 
 
 468 
 
 460 
 
 530 
 
 525 
 
 533 
 
 525 
 
 900 
 
 470 
 
 450 
 
 415 
 
 409 
 
 469 
 
 463 
 
 469 
 
 463 
 
 1000 
 
 418 
 
 
 
 376 
 
 
 
 
 
 
 
 425 
 
 413 
 
 Thus the coefficients beginning with 0C. are sensibly constant 
 for a given pressure, the same fact which was brought out by 
 Table 23 as far as the highest pressures. Hence the coefficients 
 computed for the successive intervals vary nearly inversely as 
 the successive initial volumes. This appears to be the law tow- 
 ards which the decreasing march which follows the maximum 
 points converges for conditions of increasing temperature. This 
 limiting state is reached sooner in proportion as the pressure is 
 smaller. 
 
 Hence, at all pressures and sufficiently high temperatures, 
 this simple law supervenes : the increment of volume is pro- 
 portional to increment of temperature reproducing the case of 
 perfect gases. In a general way only is the volume proportional 
 to the absolute temperature increased by a constant ; for this 
 constant diminishes as pressure decreases in such a way that if 
 pressure is small enough, the law of the proportionality of vol- 
 
 100 
 
THE LAWS OF GASES 
 
 ume and absolute temperature is encountered. This again is 
 the law of sensibly perfect gases. 
 
 COEFFICIENTS OF EXPANSION AT CONSTANT VOLUME, 
 
 1 dp dp 
 
 3 7^, AND PRESSURE COEFFICIENTS. B = -^- 
 
 p dt dt 
 
 To avoid all confusion, I will call the values j pressure co- 
 efficients. This reserves for - ~ the time-honored, but other- 
 wise very curious designation of expansion coefficient at con- 
 stant volume. 
 
 In Table 25, on page 102, computed by aid of the data in 
 Tables 6, 12, 17, 18, these coefficients are given relative to 
 the temperature interval inserted at the heads of the vertical 
 columns, and for the constant volume in the first of these 
 columns. The pressures indicated for carbon dioxide and 
 ethylene under the caption "Initial Pressures" do not all refer 
 to zero, but to the lower limit of temperature of the first mean 
 coefficient on the same horizontal row. The tables contain a 
 gap which corresponds to the region contained within the curve 
 of liquefaction. 
 
 It must be borne in mind that reduction to the unit of press- 
 ure of the coefficients /3 has been accomplished by dividing by 
 the pressure corresponding to the lower temperature of each 
 interval at variance, therefore, to the notation frequently 
 adopted. I have already made a similar remark relative to the 
 reduction of the coefficients of compressibility and of expansion 
 under constant pressure to the unit of volume. 
 
MEMOIRS ON 
 
 CQ. 
 
 ft 
 
 5 
 
 t> OO t O5 00 O i> 
 
 to 10 > os co oo co 
 
 CO CO CO CO CO CO Tj< 
 
 c o co oo oo y, 
 t- to co io ic a 
 
 r-H CO CO ^f tO O 
 
 COO500COi>COCOODT-i 
 
 8 os 01 10 t 
 r-coco co 
 
 T-I CO CO JO J> 
 
 i i 
 
 toot>S co c^Jo co^ I I 
 
 t iCOCOJOi>OCDOOi> I I 
 T- i T i CO rf 
 
 OSCOCOCOCO^COt-' 
 T-H>OJOCOZ>T-iO' 
 
 OS O OS JO 3D CO "* J> t- > I 
 
 T-iCOCOJOi>T-iJ>O500CO I 
 1-1 TH CO Tf OO 
 
 5O CD -* 
 -i-i t> O Oi 
 OS CO 
 
 O O O O O 
 OSlOt>COGQ 
 
 
 PS 
 
 iis 
 
 J> CO QO JO {> 
 00 O t- Tfi 1O 
 ^ CO CO 00 O 
 
 -r-i OS <M 
 00 T-H JO 
 Q0500 
 
 OO1OOOJO 
 O5r-iOOO'-iJO 
 
 JOO1OJO 
 
 CO 00 1-1 CO 
 
 IN i i i 
 
 ^COOOOOOOCOOOOt- 
 
 00 TO <O O 1 CO t> C^t f- * 4O O 5 OO 
 
 COr^T^S^ 10 ^ 50 ^ 051 " 
 
 102 
 
 CO T i JO C~ T-H T i CO I I 
 
 CO CO 00 JO T-< 10 CO I I 
 
 I' 
 
 ^ <* CO i> 00 i 
 
 1 1> TH co T-I as 1-1 o 
 
 > i ^ ao os 1-1 co 
 
 JO i> 00 OS O I-H O5 
 
 TH rH C CO Tt* 1O 2 
 
 JO O JO O JO O CO 
 CO CO *> -00 CO 1-1 CO 
 
 00 i i i i 1 T-HO JO 
 
 CO t- rH CO 
 
 00 ' ' ! ' O 00 O^ 
 
 10 
 
 OO 
 
 COOCOOOOCOOOC- 
 
 CO 00 CO JO rt< CO CO O7 
 
THE LAWS OF GASES 
 
 TABLE 26. VALUES OF B AND & 
 
 PRESS- 
 
 
 HYDROGEN 
 
 
 OXYGEN 
 
 UK KS 
 
 CONSTANT 
 
 
 CONSTANT 
 
 
 AT 
 ZKRO. 
 
 VOLUMES 
 
 99. '2 
 
 99.2- 200. 5 
 
 VOLUMES 
 
 99.5 
 
 99.50199.50 
 
 ATM. 
 
 FX10 
 
 5xio 3 
 
 /3X105 
 
 5X10 3 
 
 /3X10 6 
 
 rxio" 
 
 5X103 
 
 /3X105 
 
 5X103 
 
 /3X105 
 
 100 
 
 10690 
 
 373 
 
 373 
 
 366 
 
 267 
 
 9265 
 
 492 
 
 492 
 
 470 
 
 315 
 
 200 
 
 5690 
 
 766 
 
 383 
 
 742 
 
 269 
 
 4570 
 
 1226 
 
 613 
 
 1115 
 
 357 
 
 300 
 
 4030 
 
 1149 
 
 383 
 
 1129 
 
 272 
 
 3208 
 
 2090 
 
 696 
 
 1900 
 
 374 
 
 400 
 
 3207 
 
 1521 
 
 380 
 
 1475 
 
 268 
 
 2629 
 
 2924 
 
 731 
 
 2570 
 
 372 
 
 500 
 
 2713 
 
 1895 
 
 379 
 
 1842 
 
 267 
 
 2312 
 
 3698 
 
 740 
 
 
 
 
 
 600 
 
 2386 
 
 2256 
 
 376 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 700 
 
 2149 
 
 3710 
 
 371 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 PRESS- 
 
 
 NITROGEN 
 
 
 AIR 
 
 URES 
 
 CONSTANT 
 
 
 CONSTANT 
 
 
 AT 
 ZERO. 
 
 VOLUMES 
 
 99.4 
 
 99.40199.60 
 
 VOLUMES 
 
 0099.40 
 
 99.40200.4 
 
 ATM. 
 
 FX106 
 
 5X103 
 
 ,3X10* 
 
 5X103 
 
 /3X105 
 
 FXIO* 
 
 5X103 
 
 /3X1Q5 
 
 5X103 
 
 /3X105 
 
 100 
 
 9910 
 
 462 
 
 462 
 
 460 
 
 315 
 
 9730 
 
 462 
 
 462 
 
 465 
 
 319 
 
 200 
 
 5195 
 
 1075 
 
 537 
 
 1070 
 
 349 
 
 5050 
 
 1105 
 
 552 
 
 1090 
 
 351 
 
 300 
 
 3786 
 
 1748 
 
 582 
 
 1700 
 
 359 
 
 3658 
 
 1800 
 
 600 
 
 1742 
 
 364 
 
 400 
 
 3142 
 
 2382 
 
 595 
 
 2320 
 
 364 
 
 3036 
 
 2470 
 
 617 
 
 2327 
 
 360 
 
 500 
 
 2780 
 
 2982 
 
 596 
 
 
 
 
 
 2680 
 
 3085 
 
 617 
 
 
 
 
 
 600 
 
 2543 
 
 3582 
 
 597 
 
 
 
 
 
 2450 
 
 3718 
 
 620 
 
 
 
 
 
 TABLE 27. VALUES OF B AND /3 
 
 PRESS- 
 
 
 HYDROGEN 
 
 
 OXYGEN 
 
 URES 
 
 CONSTANT 
 
 
 CONSTANT 
 
 
 AT 
 ZERO. 
 
 VOLUMES 
 
 .6015.40 
 
 0047.30 
 
 VOLUMES 
 
 
 015.60 
 
 ATM. 
 
 FX10 
 
 5x103 
 
 /3X105 
 
 5X103 
 
 /3X1Q5 
 
 FX106 
 
 
 5X103 
 
 /3X10 
 
 600 
 
 
 
 
 
 
 
 
 
 
 
 2117.0 
 
 
 
 4423 
 
 737 
 
 800 
 
 
 
 
 
 
 
 
 
 
 
 1880.0 
 
 
 
 5641 
 
 705 
 
 1000 
 
 1725.0 
 
 3571 
 
 357 
 
 3467 
 
 347 
 
 1736.0 
 
 
 
 6795 
 
 679 
 
 1200 
 
 1557.5 
 
 4155 
 
 346 
 
 4017 
 
 335 
 
 1635.0 
 
 
 
 8013 
 
 668 
 
 1500 
 
 13800 
 
 5129 
 
 342 
 
 5010 
 
 334 
 
 1497.5 
 
 (1600 atm) 
 
 10513 
 
 657 
 
 1800 
 
 1258.0 
 
 5779 
 
 321 
 
 5729 
 
 318 
 
 
 
 
 
 
 
 
 
 2000 
 
 1194.5 
 
 6428 
 
 321 
 
 6342 
 
 317 
 
 1408.0 
 
 
 
 12051 
 
 602 
 
 2400 
 
 1097.5 
 
 7662 
 
 319 
 
 7315 
 
 305 
 
 1343.5 
 
 
 
 13974 
 
 580 
 
 2800 
 
 10245 
 
 8117 
 
 325 
 
 
 
 
 
 1304.0 
 
 (2700 atm.) 
 
 14423 
 
 538 
 
 PRESS- 
 
 
 NITROGEN 
 
 
 AIR 
 
 URES 
 
 CONSTANT 
 
 
 CONSTANT 
 
 
 AT 
 ZKKO. 
 
 VOLUMES 
 
 0016.0 
 
 00-43.60 
 
 VOLUMES 
 
 0015.70 
 
 00-45.1 
 
 ATM. 
 
 FX10" 
 
 5X103 
 
 /3X10 5 
 
 5X103 
 
 /3X105 
 
 FX10 
 
 5X10 3 
 
 ,3X105 
 
 5X10 3 
 
 /3X10- 
 
 800 
 
 
 
 
 
 
 
 . 
 
 
 
 2171.0 
 
 4841 
 
 605 
 
 4591 
 
 574 
 
 1000 
 
 2070.0 
 
 5500 
 
 550 
 
 5481 
 
 548 
 
 1999.0 
 
 5668 
 
 567 
 
 5543 
 
 554 
 
 1200 
 
 1946.0 
 
 6125 
 
 510 
 
 6284 
 
 524 
 
 1883.0 
 
 6051 
 
 504 
 
 6075 
 
 506 
 
 1500 
 
 1813.5 
 
 7060 
 
 471 
 
 7155 
 
 477 
 
 1754.0 
 
 7006 
 
 467 
 
 7273 
 
 485 
 
 1800 
 
 1714.5 
 
 8562 
 
 475 
 
 8440 
 
 469 
 
 1662.0 
 
 7900 
 
 439 
 
 8115 
 
 451 
 
 2000 
 
 1663.5 
 
 9375 
 
 468 
 
 9197 
 
 460 
 
 1613.0 
 
 8344 
 
 417 
 
 8736 
 
 437 
 
 2400 
 
 1583.5 
 
 10750 
 
 448 
 
 10505 
 
 437 
 
 1533.5 
 
 9681 
 
 403 
 
 9888 
 
 412 
 
 2800 
 
 1525.0 
 
 11875 
 
 424 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 103 
 
MEMOIRS ON 
 
 VARIATION OF THE COEFFICIENTS B AND /3 WITH VOLUME 
 
 The pressure coefficient B is seen to increase very rapidly 
 when volume decreases i.e., when the initial pressure at zero 
 increases. The coefficient ft (Table 25) at first increases for in- 
 creasing volume, and thereafter passes through a maximum 
 which is much less pronounced when the temperature is higher. 
 Finally ft decreases with increasing volume. In case of nitro- 
 gen the maximum is not yet reached between and 200 
 within the pressure limits given in Table 26. For hydrogen, on 
 the contrary, its occurrence falls within the -same limits, since 
 ft is then sensibly constant. For the highest pressures the 
 maximum has been passed by in case of each of the four gases 
 in Table 27. 
 
 VARIATION OF THE COEFFICIENTS AND /3 WITH TEM- 
 PERATURE 
 
 Generally speaking, the coefficient B varies very little with 
 temperature. An inspection of the table shows for carbon 
 dioxide between and 100 that this variation is quite in- 
 significant. This is the identical result reached in my re- 
 search* of 1881. Some time after Messrs. W. Ramsay and 
 Sidney Young published important researches on the same sub- 
 ject, to which I shall recur on another occasion. 
 
 Between 100 and 260, B shows a slight diminution. This 
 is also true for the case of ethylene. 
 
 For hydrogen, air, and nitrogen the variation of B between 
 and 200 (Table 26) is scarcely apparent, particularly after 
 the pressures approach the high values. A similar influence 
 may be drawn for the other three gases (Table 27) for a press- 
 ure interval quite up to the highest pressures. It must be ob- 
 served, however, that these results are restricted to smaller 
 temperature intervals. 
 
 It appears to follow from the results as a whole that the 
 variation of the pressure coefficient with temperature, always 
 very small, quite vanishes at sufficiently high temperatures and 
 probably at all temperatures under sufficiently high pressures. 
 This is evidenced by the results shown by those gases which, 
 within the temperature limits of the present research, are al- 
 
 * Annales de Chimie et de Physique, 5 e Serie, vol. xxii. 
 104 
 
THE LAWS OF GASES 
 
 ready in a thermal state far above their critical points. Under 
 these conditions the pressures corresponding to constancy of 
 volume are not proportional to the respective absolute tem- 
 peratures ; they are proportional to them when each is dimin- 
 ished by a constant function of volume only. This constant is 
 numerically a number of degrees, and it at first increases rap- 
 idly when volume diminishes ; thereafter it passes through a 
 maximum, decreases passing through zero into negative values, 
 and continues to decrease in absolute value. Whenever this 
 constant vanishes the gas is clearly characterized by the law of 
 perfect gases, and this happens in the case of hydrogen at 
 about 800 atmospheres. It is exceedingly remarkable that 
 under these special conditions the value of the pressure co- 
 efficient is nearly equal to the value which holds for normal 
 pressure i.e., to that attributed to gases when they approach 
 as nearly as possible to the state of a perfect gas. It would be 
 extremely interesting to discover whether the observation in 
 question is of general significance. Unfortunately, the other 
 gases studied have not under the highest pressures applied 
 reached the state for which the constant in question vanishes. 
 
 The variations of the constant ft may be deduced from what 
 has just been stated. In every case this coefficient for a given 
 volume varies very nearly inversely to pressure. In the region 
 comprised within the curve of liquefaction, and corresponding 
 to the gap in Table 25 (carbon dioxide), there is no true pressure 
 
 coefficient. The values - now refer to the maximum vapor 
 
 tl t 
 
 tensions and no longer vary with volume. Necessarily an 
 abrupt variation of these values occurs on breaking across the 
 curve of liquefaction, excepting, perhaps, the line of equal vol- 
 umes, which passes through the critical point with an inver- 
 sion of the sign of the variation on one side or the other of this 
 
 line. Indeed, it is easily observed that the values of yr for the 
 
 lines of equal volume passing above the critical point and near 
 the curve of saturation are smaller on the outside than on the 
 inside of this curve. The contrary will be the case for the 
 lines of equal volume which pass below the critical point. In 
 every case the above inferences relative to pressure coefficients 
 seem to be immediately applicable as soon as the curve of 
 liquefaction is left behind. 
 
 105 
 
MEMOIRS ON 
 
 The isotherms below the critical point are difficult to map 
 out in those parts which are contiguous with the curve of 
 liquefaction. This curve cannot be obtained by means of the 
 above experiments as accurately as may be done by comparing 
 the densities of the liquid and of the vapor obtained in experi- 
 ments specially designed for this purpose. I have carried out 
 measurements of this kind for carbon dioxide between zero and 
 the critical point; but I will not enter into details relative to 
 these results,* as they lie outside of the scope of the present in- 
 vestigation, beyond giving a tabulated view of the data. The 
 agreement between the present values of maximum vapor tension 
 and those contained in the above tables is apparent. The same 
 research furnished the following elements of the critical point : 
 
 Critical temperature 31.35 
 
 Critical pressure 72.9 aim. 
 
 Critical density 0.464 
 
 TABLE 28. DATA FOR CARBON DIOXIDE 
 
 
 DENSITY OP THE 
 
 
 
 DENSITY OP THE 
 
 
 
 
 MAXIMUM 
 
 
 
 MAXIMUM 
 
 T 
 
 LIQUID 
 
 VAPOR 
 
 VAPOR 
 TENSION 
 
 T 
 
 LIQUID 
 
 VAPOR 
 
 VAPOR 
 TENSION 
 
 Deg. 
 
 
 
 Aim. 
 
 Deg. 
 
 
 
 Atm. 
 
 
 
 .914 
 
 .096 
 
 34.3 
 
 18 
 
 .786 
 
 .176 
 
 53.8 
 
 1 
 
 .910 
 
 .099 
 
 35.2 
 
 19 
 
 .776 
 
 .183 
 
 55.0 
 
 2 
 
 .906 
 
 .103 
 
 36.1 
 
 20 
 
 .766 
 
 .190 
 
 56.3 
 
 3 
 
 .900 
 
 .106 
 
 37.0 
 
 21 
 
 .755 
 
 .199 
 
 57.6 
 
 4 
 
 .894 
 
 .110 
 
 38.0 
 
 22 
 
 .743 
 
 .208 
 
 59.0 
 
 5 
 
 .888 
 
 .114 
 
 39.0 
 
 23 
 
 .731 
 
 .217 
 
 60.4 
 
 6 
 
 .882 
 
 .117 
 
 40.0 
 
 24 
 
 .717 
 
 .228 
 
 61.8 
 
 7 
 
 .876 
 
 .121 
 
 41.0 
 
 25 
 
 .703 
 
 .240 
 
 63.3 
 
 8 
 
 .869 
 
 .125 
 
 42.0 
 
 26 
 
 .688 
 
 .252 
 
 647 
 
 9 
 
 .863 
 
 .129 
 
 43.1 
 
 27 
 
 .671 
 
 .266 
 
 66.2 
 
 10 
 
 .856 
 
 .133 
 
 44.2 
 
 28 
 
 .653 
 
 .282 
 
 67.7 
 
 11 
 
 .848 
 
 .137 
 
 45.3 
 
 29 
 
 .630 
 
 .303 
 
 69.2 
 
 12 
 
 .841 
 
 .142 
 
 46.4 
 
 30 
 
 .598 
 
 .334 
 
 70.7 
 
 13 
 
 .831 
 
 .147 
 
 47.5 
 
 30.5 
 
 .574 
 
 .356 
 
 71.5 
 
 14 
 
 .822 
 
 .152 
 
 48.7 
 
 31.0 
 
 .536 
 
 .392 
 
 72.3 
 
 15 
 
 .814 
 
 .158 
 
 50.0 
 
 31.25 
 
 .497 
 
 .422 
 
 72.8 
 
 16 
 
 .806 
 
 .164 
 
 51.2 
 
 31.35 
 
 .464 
 
 .464 
 
 72.9 
 
 17 
 
 .796 
 
 .170 
 
 52.4 
 
 
 
 
 
 * Gomptes Rendus, May 16, 1892 ; June 7, 1892. 
 1892; Seances de la Soc. de Physique, 1892. 
 
 106 
 
 Cf. Journal de Physique, 
 
THE LAWS OF GASES 
 
 I have not up to the present time been able to repeat the 
 same work for ethylene. 
 
 Certain other properties of the isotherms for carbon dioxide 
 and ethylene, as well as divers inquiries of a more theoretical 
 kind, are not in place here. In the present memoir, as well 
 as in the following work relating to liquids, I have purposed 
 merely to exhibit the experimental methods, to 'publish the 
 numerical results obtained, and to deduce from them such gen- 
 eral laws as result from inspection. 
 
 EMILE HILAIRE AMAGAT was born on the 2d of January, 
 1841, at St. Satur, a village in the arrondissement de Sancerre, 
 in the Departement du Cher. It was at first his intention to be 
 a technical chemist, but he abandoned this career almost at the 
 very outset in preference of one in pure science. 
 
 For several years Amagat was preparateur of the celebrated 
 Berthelot at the College de, France. After this (between 1867 
 and 1872) he was called to Switzerland, where he served as pro- 
 fessor at the Lycee de Fribourg. It was there that Amagat com- 
 pleted his these de doctoral, being formally honored with this 
 degree in Paris in 1872. 
 
 Returning to France, he was successively made professor at 
 the Lycee d'Alencon, a I'Ecole Normale Specialede Cluny, and in 
 1877 was appointed professor of physics in i\\e Faculte Libre des 
 Sciences of Lyons. In this institution, then merging into active 
 existence, he created the department of physics, and in it con- 
 ducted his most famous researches. 
 
 He left Lyons in 1891 for Paris, where he resides at present 
 in the official position of examinateur a I'Ecole Poly technique. 
 
 Amagat has been correspondent of the Institut de France 
 (Academic des Sciences, Section de Physique) since 1889. He 
 was elected a foreign member of the Royal Society of London 
 in 1897, and of the Royal Society of Edinburgh in the same year. 
 He is honorary member of the Societe Hollandaise des Sciences, 
 of the Societe Scientifique de Bruxelles, of the Philosophical 
 Society of Manchester, etc., etc. 
 
BIBLIOGRAPHY 
 
 AMONG Amagnt's papers those bearing particularly on the laws of gases 
 may be summarized for the reader's convenience as follows. A complete 
 list of Amagat's researches will be found in a pamphlet published by 
 Gautier-Villars et tils, Paris, 1896, entitled: Notice sur les Travaux Scien- 
 (ifiques de M. E. H. Amac/at. 
 
 De {'influence de la temperature sur les ecartes de la loi de Mariotte ; C. JR., 
 
 Ixviii., p. 1170, 1869. 
 
 Sur la compressibilite du gaz ; C. R., Ixxi., p. 67, 1870. 
 Sur la dilatation et la compress, des gaz ; C. R., Ixxiii., p. 183, 1871. 
 Sur la compress, de 1'hydrogene et de 1'air a des temperatures elevees ; 
 
 C. R., Ixxv., p. 479, 1872. 
 
 Sur la dilatation des gaz humides; C. R., Ixxiv., p. 1299, 1872. 
 Compress, de 1'air et de 1'hydrogene a" des temperatures elevees ; Annales 
 
 de Chimie et de Physique (4), xxviii., 1873. 
 Dilat. et compress, des nz a divers temperatures ; Annales de Chimie et de 
 
 Physique (4), xxix., 1873. 
 Recherches sur 1'elasticite de 1'air sur de faibles pressions ; G. R., Ixxxii., 
 
 p. 914, 1876 ; ibid., Annales de Chimie et de Physique (5), viii., 1876. 
 Sur la compress des gaz a depressions elevees ; C. R., Ixxxvii., p. 432, 
 
 1878. (Preliminary work at Fort Saint-Just.) 
 Experiences du puits Verpilleux ; C. R., Ixxxviii., p. 336, 1879. 
 Sur la compress, des divers gaz a des pressions elevees; C. R., Ixxxix., 
 
 p. 439, 18^9. 
 
 Influence de la temperature sur la compress, des gaz sous de fortes pres- 
 sions; C. R., xc., p. 994, 1880. 
 Sur la dilatation et la compress, des gaz sous de fortes pressions ; C. R., 
 
 xci., p. 428, 1880. 
 Sur la compress, de I'oxyire'm', et 1'action de ce gaz sur le mercure, etc.; 
 
 C. R., xci., p. 812, 1880. 
 Sur la compress, de 1'acide carboniqtie et de 1'air sous t'aible pression et 
 
 temp, elevee ; G. R., xciii., p. 306, 1881. 
 Memoire sur la compressibilite des g?iz aux fortes pressions ; Annales de 
 
 Chimie et de Physique (5), xxii., 1881. 
 Sur la relation (p, v, t')=0 relative aux gaz, etc. ; C. R., xciv., p. 847, 
 
 1882. 
 
 Sur 1'elasticite des gaz rarefies ; C. R., xcv., p. 281, 1882. 
 Sur .... la compress, du gaz azote ; C. R., xcv., p. 638, 1882. 
 
 108 
 
MEMOIRS ON THE LAWS OF GASES 
 
 Sujets relatifs a 1'etude du gaz ; Annales CMmie et de Physique (5), xxviii., 
 
 1883. 
 Memoire sur la compress, de Pair et de 1'acide carbonique . . ; Annales de 
 
 CMmie et de Physique (5), xxviii., 1883. 
 Memoire sur la compress, de Fair, de 1'hydrogene et de 1'acide carbonique 
 
 rarefies ; Annales de Chimie et de Physique (5), xxviii., 1883. 
 Sur une forme nouvelle de la fonction (p, v, t)=Q ; Annales de Chimie 
 
 et de Physique (5), xxviii., 1883. 
 Resultats pour servir aux calculs des manometres a gaz ; C. R., xcix., 
 
 p. 1017, 1884. 
 
 Note relative a une erreur . . . . ; C. R., xcix., p. 1153, 1884. 
 Sur la densite liraite et de volume atomique des gaz, etc.; C. R., c., p. 633, 
 
 1885. 
 
 Sur la volume atomique de 1'oxygSne ; C. It., cii., p. 1100, 1886. 
 Compressibilite des gaz : oxygene, hydrogene, azote et air jusqu'a 3000 
 
 atm.; C. R., cvii., p. 522, 1888. 
 Nouvelle methode pour 1'etude de la compress, et de la dilatation des 
 
 liquides et des gaz . . . . ; C. R., cxi., p. 871, 1890. 
 Sur la determination de la densite des gaz etde leurvapenr snturee . . . . ; 
 
 C. R., cxiv., p. 1093, 1892 ; ibid., C. R., cxiv., p. 1322, 1892 ; Journal 
 
 de Physique, p. 288, 1892. 
 Sur les lois de dilatations des gaz sous pression constante ; C. R., cxv., 
 
 p. 771, 1892. 
 Sur la comparaison des lois de dilatation des liquides et de celles des 
 
 gaz, etc.; C. R., cxv., p. 919, 1892. 
 Sur les lois de dilatation a volume constant des fluides . . . . ; C. R., cxv., 
 
 p. 1041, 1892. 
 Memoires sur 1'elastioite et la dilatation des fluides jusqu'aux tre"s hautes 
 
 pressions ; Annales de Chimie et de Physique (6), xxix., 1893. 
 Sur la pression interieure dans le gaz ; C. R., cxviii., p. 326, 1894 ; ibid., 
 
 C. R., cxviii., 566, 1894. 
 
 Sur la pression interieure et le viriel . . . . ; C. R., cxx., p. 489, 1895. 
 Verification d'ensemble de la loi des etats correspondants de Van der Waals; 
 
 C. R., cxxiii., p. 30, 1896 ; ibid., C. R., cxxiii., p. 83, 1896. 
 
 The titles of a few relevant papers by other investigators follow: 
 
 RELATIONS BETWEEN PRESSURE, VOLUME, AND TEMPERATURE 
 
 Ramsay and Young, Philosophical Transactions, 177, 178, 18O, 183. 
 
 Barus, C., Philosophical Magazine (5) 3O, 338-361, 1890.- 
 
 Tait, P. G., "Challenger Reports," Physics and Chemistry, vol. ii., 
 
 part iv. ; Proceedings of tlie Royal Society of Edinburgh, 
 vols. xii. , xiii., xx. 
 Leduc, A., Journal de Physique (3), 7, 1898. 
 
 Annales de Chimie et de Physique, 15, 5-115, 1898. 
 Wroblewski, Wiedemann, Annalen, 29, 428, 1886. 
 Rose-Innes, Philosophical Magazine, 44, 45, 1897, 1898. 
 
 109 
 
MEMOIRS ON THE LAWS OF GASES 
 
 CONTINUITY OF LIQUID AND GASEOUS STATES 
 
 Van dor Waals, "On the Continuity of the Liquid and Gaseous States." 
 Translation. London, 1890. (Original Dutch edition, 
 1873.) 
 
 Clausius, R., Wiedemann, Annalen, 9, 337, 1880. 
 
 Sarrau, Comptes Rendus, 1 1O, 880, 1890. 
 
 Ramsay and Young, Philosophical Magazine (5), 23, 24, 1887. 
 
 Brillouin, M., Journal de Physique (3), 2, 113, 1893. 
 
 Tait, P. G., Transactions of the Royal Society of Edinburgh, 36, 1891. 
 
 Nature, 44, 45, 1891. 
 
 Rayleigh, Lord, Nature, 44, 45, 1891. 
 
 Bakker, G., Zeitschrift filr Physikalische Chemie, 21, 127, 1896. 
 
 Young, S., Philosophical Magazine (5), 33, 153, 1892 (37, 1, 1894). 
 
 CRITICAL STATE 
 
 Andrews, Philosophical Transactions, 166, 421-449, 1876. 
 
 Cailletet and Colardeau, Annales de Chimie etdePhyxique(}, 25, 519, 1892. 
 Mathias, E., Journal de Physique (3). 1. 53, 1892. 
 Kuenen, J. P., Philosophical Magazine, 44, 1897. 
 
 THE END. 
 
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