1 86 



NA TURE 



{_Dc 



1880 



of voyages of d iscovery made during antiquity and the middle 

 ao-es as far as Magellan's first voyage round the globe, will be 

 shortly published by Herr Spamer of Leipzig. It will contain 

 some 100 illustrations, besides maps, charts, &c. 



CRITICAL TEMPERA TURE OF ETHYLENE 



MAMAGAT (CiJOT/A r.nd.'' [1S79], Ixxxix. p. 437, corrected 

 • Bcibldtlcr\\%%6\, iv. p. 19) has ^uimiitted hydrogen, oxygen, 

 nitrogen, air, carbon monoxide, methane, and ethylene at tempera- 

 tures from 18° to 22° to pressures ranging between 28 and 43 1 atmo- 

 spheres, and finds that, except for hydrogen, the product /f f;r^t 

 diminishes and then increases as/ increases, the most marked 

 case being that of ethylene, for which the values of / 1/ at 31 'SS, 

 84-16, 39S71 atmospheres are proportional to 2'29, i, 3-13 

 respectively. Dr. van der Waals deduced this general pecu- 

 liarity theoretically in 1S73, and showed that its markedness is 

 the greater, the less the temperature of compression exceeds the 

 critical temperature : concluding, therefore, that for ethylene 

 the critical temperature is not far belo.v iS°, as M. Amagat has 

 also surmised, he has recently (Meded. der k . Akad. van U'cten- 

 schappcn in Amsterdam, Mei 18S0)- determined it directly by a 

 Cailletet compression-apparatus, finding it to be 9°'2, and the 

 critical press \re 58 atmospheres. 



On p. 55 of his dissertation "Overde Continuiteit van den 

 Gas- en Vloeistoftoestand " (Leiden, 1S73), van der Waals finds 

 the characteristic equation of a gas in the form — 



(/ + ,g(- 



h] = R{I + af), 



where a, h, R are constants and o" the coefficient of expansion, 

 and on p. 79 d seq. it is shown that at the critical temperature 

 all three values of v given by this equation, which may be 

 written 



- \ , R(i -V o.{)\ „ , a ab 



V - { + — ' i ZJ- + ^7/ - =0, 



( / s / / 



are equal ; hence, if Vh put for this common value of f, and 

 T, P for the corresponding values of /, p, i.e. for the critical 

 temperature and pressure, the theory of equations gives 



ab 



2V^b + ^^», 3^= = |, F3 = _, 



whence 



P-. 

 and also 



2']b''' 



lb, PV = 



%a 

 2^bR' 



a = 2,PV% b = lV, R = %-^^-^. 

 I + a 1 

 The minimum value of /z/ at any temperature / may be de'.er- 



mined in the usual way by ■ 



; equated to zero, and, if 



p', 'J are written for the corresponding values of/, v, there resulj 

 ^' ,/' = 27(1 - t)(2t - l)/',/'e;' = 2{2T- ij/T, 



■where 



3(1 



hR(i +a/) ^ 



I + 



a -' I -)- a r 



Thus a minimum value oi pv exists only when 



I > T > i, 

 i.e. only at temperatures that lie between 



a _ \ ] a _ I 

 bin a "° 4 * K a V 

 If /i represents the pressure of the gas when occupying unit 

 volume at /, then 



(A + «)(i - ^)^^(l +«0, 

 and, /i being the value of / z/ in this initial state, the markedness 

 of the minimum value oi pv is greater the less 



p'-J ., • , ^ (l - b\(ZT - l) 



< — or Its equivalent ^ ^ :, 



/i ' T= - b{\ - b) 



that is, since the sign' of the /-differential coefficient of this 

 expression is the same as that of (t - ^) (l - ^ - t), the less ;■, 

 provided that 



I - b > r > b, 



' Since the following was written, M. Amagat has published further re- 

 sults, which do not however affect its main point. 



^ Mr. Dickson seems to have independently discovered (P/iil. Mag. for 

 July, 1880) the principles laid down by Dr. van der Waals in his above 

 mentioned dissertation, pp. 79-93, which is not sufficiently known in England' 



or that the temperatures lie between 



«(I - I')- I ._j ab 



If 7J represents the volume of the mass of gas which occupies 

 unit volume at o" under unit pressure, then 



R=(i+a)(i-b), 

 as is taken in the following calculations. 



In the case of ethylene van der Waals' experiments give 

 7'= 9-2 and j°=58: hence, by the above relations -wltb 

 a = o '00367, 



which lead to a cubic equation tliat gives 



a = o'oo7S6, b = 0*00224, P = I •0056, 

 so that the characteristic equation is 



^ (Voo37(272' 5 + /) _ 0-00786 

 - 0-00224 ^'-^ ' 



/^ 



the pressure being reckoned in atmospheres ; hence too 

 V — o-oo57 and p F ■— 0-39. Further, when t = 20, the mean 

 temperature in Amagat's experiments, t = 0-5547, and thus by 

 calculation/' = 76-25, while Amagat's direct observations give 

 /■ = 84 approximately, £0 far justifying the the theory. The 

 temperatures for which pv has a minimum value range from 

 678" to - 35°. 



The intimate agreement between Amajat's experiments and 

 van der Waals' formula (which is entirely independent of them) 

 is shown by the following table, wherein the first column con- 

 tains the pressures (expressed in atmospheres) employed ,by 

 Amagat, the second his experimental values of pv divided by 

 23500, and the third the values of pv calculated for / = 20 

 from the formula : — 



The only serious discrepancy occurs for / = 59-38, and van 

 der Waals accounts for this by supposing that in Amagat's table 

 12263 is misprinted for 15263, so that the asterisked number 

 shoitld be 0-650 ; for by experiment he finds that the ratio of 

 the values of pv for/ = 45 -So and/ = S9-38 is 1-26 (the calcu- 

 lated ratio being 1-25), while Amagat's actual utimbers give 

 1-50, but, when corrected, I -20. 



For methane the equation of van der Waals' form that best 

 satisfies Amagat's experimental values has for constants 

 fl = 10" X 2-9, ^ = S3, R = 25525, if / = 20, a = 0-00367, 

 pressures being measured in metres of mercury, and this gives 

 ~99i° foi- the critical temperature and 50J atmospheres for the 

 critical pressure. The constants have large values here, for, as 

 calculation shows, the mass of the gas considered is about 

 24^- grams, which would occupy, at 0° under one atmosphere, 

 about 33518 c.c. 



This discussion — with the numbers recalculated — by Dr. van 

 der Waals of M. Amagat's experiments in connection with the 

 critical temperature is here reproduced, together with the brief 

 ic'siini^ of his theory (which has not hitherto a|ipeared in an 

 English dress), for ready application in other cases. 



September 17 Robert E. Baynes 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE 

 Cambridge. — The Natural .Science Tripos Class List has just 

 been issued. There are eight names in the first class, eight in 

 the second, and fifteen in the third. Of those in the first class 

 three attain their fir»t class for Physics and Chemistry, viz. : 

 Fleming, St. John's (distinguished in Physics) ; S. L. Hart, St. 

 John's, and Heycock, King's. Two attain their first class for 



