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148 I . M. Abdulagatov and S. M. Rasulov: Viscosity of N-Pentane, N-Heptane and Their Mixtures

Viscosity of N-Pentane, N-Heptane and Their Mixtures within the TemperatureRange from 298K up to Critical Points at the Saturation Vapor Pressure

I.M. Abdulagatov and S.M. Rasulov

Institute for Geothermal Problems of the Dagestan Scientific Center of The Russian Academy of Sciences, 367030 Makhachkala,Kalinina 39-A, Dagestan, Russian Federation

Key Words: Critical Point / Mixtures / N-Pentane / N-Heptane / Viscosity / Saturation Line

The viscosity of n-pentane, n-heptane and their mixtures has been measured with a capillary flow method be-tween 298 K and t he critical temperatures at t he sat uration vapor pressure. The concentrations studied were 0.259,0.419 and 0.745 mole fraction of n-heptane. T he maximal error of the experimental values of the viscosity is esti-mated to be 1.2 in the region far from the critical point and k5vo in the immediate vicinity of t he criticalpoint. T he viscosity obtained was compared to da ta by othe r autho rs with satisfact ory agreement. The validityof the method has been confirmed by the measurement of the viscosity of standard liquids as water and toluene.

1. Introduction only a limited amount of data is available [I 291. Inpapers [12-14, 18, 24, 25, 32-37] the viscosities ofgaseous n-pentane and n-heptane were measured in the tem-perature range from 298 576 K at atmospheric pressure.

The viscosities of liquid n-pentane and n-heptane at atmo-spheric pressure has been measured in papers [l o, 15 17,261 at temperatures from 292 K to 346 K. The measure-ments were obtained with different techniques. The viscosi-

N-pentane and n-heptane has been investigated by a num-ber of authors [I 371. In Tables 1 and 2 selected primary

data sets are collected with their individual pressure andtemperature ranges, the experimental method used and theiruncertainty. Most of the measurements were performed atatmospheric pressure [ lo 20, 32 371. At higher pressures

Table 1

Primary experimental data for the viscosity of n-pentane and n-heptane at atmospheric pressure

Reference Technique Temperatu re range State[KI

Uncertainty[ I

n-PentaneTitani [I21Bleakney [141Lambert et al. [36]

Sage and Lacey [18]Agaev et al. [24]McCoubrey et al. [32]Diaz Pena et al. [33]This paperShepard et al. [ I S ]Agaev et al. [24]Geist and Cannon [I61Khalilov [21]Thorpe and Rodger [I71Oliveira et al. [ lo ]This paper

n-HeptaneMelaven and Mack [37]Lambert et al. [36]Agaev et al. [25]Carmichael et al. [35]Diaz Pena et al. [34]This paperKnapstad et al. [26]Kashiwagi et al. [4]Assael et al. [ I ]Khalilov [2]Golubev [3]This paper

Day [I31

CRCC, ODRCRBCCCCCCCCCvwC

CC, ODCRCCCocTCvwCCC

395 576298, 373

298308 363

298 523298 548303 363295 423322 524298298293

303 348303298

293 353

313 524338 363373 474294 377333 423314 550292 346298 348303, 323297 51 3183 53298 350

GasGasGasGasGasGasGasGasGasLiquidLiquidLiquidLiquidLiquidLiquidLiquid

GasGasGasGasGasGasLiquidLiquidLiquidLiquidLiquidLiquid

1

3

22121.211

0.5

0.51.2

1

31.6

21.20.623

1.61.2

VW, Vibrating wire; C, Capillary; RC, Rotating cylinder; FB, Falling body; OD, Oscillating disk; RB, Rolling ball; OC, Oscillating cylinder;TC, Torsional crystal

Ber. Bunsenges. Phys. Chem. 100, 148-154 1996) No. 2 CH Verlagsgesellschaft mbH, 0.69451 Weinheim, 1996 0005-9021/96/0202-0148 S 10.00+ . 2 5 / 0

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I M. Abdulanatov and S. M. Rasulov: Viscosity of N-Pentane, N-HeDtane and Their Mixtures 149

Table 2Primary experimental data for the viscosity of n-pentane and n-heptane under pressure

Reference Technique Temperature range Pressure range Uncertainty

[Kl [MPal [0701

n-PentaneSage et al. [I81Golik et al. [22]

Hubbard et al. [I91Remer et al. [20]Collings et al. [29]Khalilov [21]Bridgman [23]Agaev et al. [24]Oliveira et al. [lo]Brazier et al. [30]This paper

RBFB

RBRCTCCFBCvwRBC

n-heptaneKashiwagi et al. [4] TCAssael et al. [I] vwKhalilov [2] CGolubev [3] CAgaev et al. [25] C

This paper C

300 377283 -473

298 523311-411303, 323

303, 348

303, 323303, 323

373 -423

298 548

298 524

298 348303, 323293 5 13323 - 573298 548

298 550

14

735200

I20050

252250

50

ps

11070

6050

50

ps

0.52

221

21.60.50.5I .2

20.5

1.61.6

1.2

VW, Vibrating wire; C, Capillary; RC, Rotating cylinder; FB, Falling body; OD, Oscillating disk; RB, Rolling ball; TC, Torsional crystal;OC, Oscillating cylinder

ty of n-pentane and n-heptane under pressure was measuredfor temperatures between 298K and 423 K at pressures upto 252 M P a in work s [I , 18 5, 28 301. How ever, theearlier measurements for pure components did not extendto the satura tion lineso that a modest extrapolat ion to thesaturated vapor pressure has been necessary.

An extensive review of the viscosity data of gaseoushydrocarbons at atmospheric pressure has recently beenpresented by Tarzimanov et al. [34]. In the literature, forthe binary mixtures of n-pentane-n-heptane viscosity dataare lacking. The purposeof this work is to providea reliableset of (viscosity q , pressure P , temperature 7 ) alues forpure n-pentane and n-heptane along the saturatio n lines andtheir mixtures along the dew point a nd bubb le point l ines,to extend the temperature range and to complete prelim-inary results reported earlier.

2. Experimental

Th e viscosity was mea sured witha capillary -flow viscom-

eter. A schematic diagramof the experimental apparat us isshown in Fig. 1. The apparatus consists of the followingmain par ts , a high-pressure viscometric vessel 1, acapillary viscometer 2,a copper block 3, a heater4 , a stainless steel1 ac ket 5 , two connecting high-pressurevessels 6, and a frequencymeter (FM-5041) 7. Th e vis-cometer is mounted inside a high-pressure viscometricvessel. Th e viscometric vessel is ma deof type 321 stainlesssteel and ha s a length of 265 mm an d an inner diameterof18 mm and outs ide diameterof 66 mm. A massive copperblock 3 is slipped over the high-pre ssure steel vessel byhot pressing in order to impro ve the temperature con trol. Astainless steel jacket is put over the copper block by means

4

Fig. 1Schematic diagram of the experimental apparatus for high-temperatureand high-pressure measurements of the viscosity. High-pressureviscometric vessel 1; capillary viscometer 2; copper block 3;heater 4; stainless steel jacket 5; two connecting high-pressurevessels 6 ; frequencymeter (FM-5041) 7

of hot pressing. The whole system is covered witha thicklayer of glass cloth fro m the outside for better h eat insula-tion.

Fig. 2 shows the co nstruction an d geometric characteris-tics of the viscom eter. The viscometer consistsof a lowerbulb 1 a connecting tube 2, a preliminary bulb 3,a measuring bulb 4,a capillary 5, and plat inum con-tacts 6. The viscometer was mad e fro m refractory glass(supremax) . The capi l lary has a length of 50mm andadiameter of 0.10 mm . The lengthof the capillary is measur-ed with a cathetometer whose accuracy for each end is

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150 I. M. Abdulagatov and S . M. Rasulov: Viscosity of N-Pentane, N-Heptane and Their Mixtures

Fig. 2Construction and geometric characteristics of the high-pressure capilla-ry viscometer. Lower bulb 1 ; connecting tube 2; preliminary bulb

3; measuring bulb 4; capillary ; platinum contacts 6

abou t 0.1 mm. To examine the uniformity, roundness andstraightness of a glass capillary, an optical method wasused. A glass capillary is filled with mercury and immersed

in a l iquid with a refractive index nearly equal to thatof acapillary material. Th e changes of diameterof the m ercurythread ar e then determinedat various points with the aid ofa microscope. The volumes of the prel iminary a nd m easur-ing bulbs of the viscometer were determined by the mer-cury-weighing me thod . T he heightof the mercury columnin the viscometer an d the difference of the m ercury levelscorresponding to the beginning and the endof the mercuryflow from the measuring bulb were determined by thecathetometer.

The t ime of mercury f lowing from the upper contactofthe measuring bulb to the lower bulb was measured auto-matically by a frequencymeter (FM-5041) with a n accuracyof k 1 ms. The upper contact of the viscometer was con-nected to brand s tar t and the middle to brand s top.The measurement of the flow time was repeated6 7 timesfor each temperature a nd pressure in orderto confirm thereproducibili tyof the results. The flow time f or the investi-gated hydrocarbons was more tha n220 s. The dead-weightgauge (MP-600) was used to generate and to measure thepressure.

The accuracy of the measurem ents of pressure was esti-mated to be k 1.5 kP a. Th e temperature was measured witha pla t inum resis tance thermometer (PTR-10N4419). Theuncertainty of the temperature measurements is estimated

to be less thank

15 mK. The temperatureof th e high-pres-sure viscometric vessel contai ning the ca pillary viscometer iscontrolled by means of a high-precision tempe ratureregulator (HPTR -3). The temperature of the viscometer waskept con stant to within k 10 mK. Fig. 2 shows the principleof op eration of the capillary viscometer. Initially mercury isin the lower bulb 1 (positionA . When the high-pressureviscometric vessel 1 (Fig. 1) is turn ed by a n angle of90the viscometer is in a horizon tal position (position-B) andthe mercury spills over the whole viscometer. When theviscometer returns to its initial vertical position-C, the levelof mercury will be higher tha n the upper con tact. Du e to thedifference of the m ercury levels in th e viscometer, flowof

the fluid throu gh the cap illary takes place. Wh ile lowering,the mercury successively disconnects contacts at the inletand the out le t of the measuring bulb 4 and the f low timeis fixed.

The plat inum contactsof the viscometer a re welded t o in-sulated nichro me w ires witha diameter of 0.2 mm which areconnected t o th e ou ts of the pressure vessel by a n electricallyinsulated feed-throug h. The viscometer is fixed to the feed-throu gh a nd installed in the high-pressure vessel which canbear pressures of m o r e t h a n 1 0 0 M P a .

The viscosity w as calculated from equation :

with

H1-H2 . hHl HO

H,=- , a = - - ,In

H2

Vo = 1.1444k 0.0001 cm, Ho = 57.938 k 0.029 m m ,a = 0.83872+0.00056, where g = 9.81 m . C 2 is t he a c-celeration due to gravity, Ro a n d Lo are the radius andlength of the capi l lary a t room temperature;a is the coeffi-

cient of linear expansion of the capillarys glass;A T = (7- To) is the difference between the experimentaltemperature T and room temperature To =293.1 5 K;p ( T, P ) n d po(To,P) re th e densities of the sample a t theexperimental conditions T , P ) and a t room tempera tu reand experimental pressure (To, ) ; p (To, P ) a n dpo*(To,O.l MPa) are the densi ty of the mercury a t roomtemperature and exper imental pressure and atmosphericpressure, respectively; r is the kinetic-energy correctionfactor m = 1.12) ; Vo s the volume of the sample flowingthrough the capi l lary a t room temperature; andz is the ef-flux time; H , a n d H2 are th e heightsof the mercury columnin th e viscometerat the beginning and the end ofa measure-

ment ; h is the height of the mercury column in the lowerbulb. The valuesof H , , H 2 , L , , L 2 , h are given in T able3 .In Eq. (1) the pressure difference between th e two en dsofa capillary, AP, has been replaced by the mea n hydrostaticpressure, A P = @ - p ) g A in which p is the density of the

Table 3Values of the geometric characteristics of the viscometer

H , / m m H,/mm L,/mm L2/mm h / m m

77.1744 42.1999 107.9337 84.1140 48.5941

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I52 1. M. Abdulagatov and S. M. Rasulov: Viscosity

Table 5The viscosity of n-pentane in the liquid ( q ' ) and vapour (q ) phasesalong the saturation line

of N-Pentane, N-Heptane and Their Mixtures

Table 7The viscosity of a 0.581 n-pentane-0.419 n-heptane mixture along thedew point (q ) and bubble point ( q ' ) lines

T P P' q'.104 q f t . o4 p i P[K] [MPa] [MPa] [P a. s] [ Pa. s] [ kg .m- 3] [ k g . ~ ~ ~ ]

298313

333353373393413423433443453459463466468469469.60

469.95

0.0670.114

0.2120.3630.5830.8871.3201.579I .8742.2082.5662.8102.9823.1133.2103.2623.286

3.330

0.21550.1905

0.16170.13540.1 1410.09610.08050.073 10.06520.05770.05000.04560.04180.03930.03640.03420.0325

0.0263

0.0070

0.00750.00810.00870.00940.01030.01070.01 140.01250.01430.01540.01670.01860.02020.02200.0239

0.0263

621.3606.2

585.0562.4537.7510.7478.7460.4439.4416.1386.7364.3344.5325.3306.5291.5280.9

232.0

3.36

6.0210.116.325.038.647.659.173.593.5

110.9126.9144.0160.9174.6184.1

232.0

Table 6The viscosity of a 0.741 n-pentane-0.259 n-heptane mixture along thedew point (a ) and bubble point (q ) ines

T P P' , 1 J . ~ 0 4 q r r to4 p ' P[K] [MPa] [MPa] [Pa.s] [Pa.sl [ k g . r ~ - ~ ] kg.m-3]

443453463473483488490491491.6492.6

1.3421.5841.8972.2502.6842.9683.0633.1223.1623.320

1.686I .9652.2572.6033.0123.2133.2803.3093.3283.320

0.75550.68400.61450.54600.46650.40900.37900.35500.33600.2650

0.11350.12210.13620. I5480.18000.20050.21700.23350.25100.2650

467.0449.0424.0382.5346.0323.2307.0296.0233.0

42.852.566.183.8

114.2139.0154.9164.5169.0233.0

o

-@L0.8

0.6

0.4

0.2 r

L

450 5 550

Tern p e a u e / KFig. 3Viscosity of pure n-pentane and n-heptane as functions of temperaturealong the saturation lines. 1 Pure n-pentane; 2 - pure n-heptane

463 1.492413 1.806

483 2.145488 2.331493 2.534497 2.716499 2.818501 2.923503 3.034504 3.084504.6 3.115505.0 3.308

1.8952.191

2.5202.6962.8773.0273.0983.1753.2513.2683.2763.308

0.70200.6341

0.57000.53600.49700.45770.43500.40950.37950.35800.33500.2660

0.11900.1280

0.14250.15350.16730.18200.19150.20100.21850.23350.24700.2660

458.0441.0

419.5406.5387.7365.5349.0328.1299.0281.5270.0233.5

47.660.0

77.087.5

100.5113.4121.2131.4144.0153.0159.0233.5

with values considered as stand ard da ta[I 1, is goo d an dsufficient to confirm th e validity of our meth od. The

viscosities calculated from the working Eq.(1) for n-hep-tane , water a nd toluen e agree d with the reference viscositiesto within t 0 . 5 Vo . The deviations are well within th e mutu alerror l imits. Near th e crit ical point i t is difficult to keep theflow in a lamina r co ndition since the kinematic viscosity isvery low. The flow rate mu st therefore be kept sufficientlysmall to maintain the Reynolds number a ta sufficien tly lowvalue.

The hydrocarbons were purified by double disti l lation.We estimate the final purity of our hydrocarbons to be99.98 mass per cent by gas chromatograp hy. F or bo th fluidsand their mixtures, samples were taken from the cell afterthe measurements a nd were again analyzed. There was noevidence of any change in the levelof impurities.

3. Results and Comparison

The measured values of the viscosityof pure n-pentane,n-heptane along the saturation line and the three binarymixtures of n-pentane-n-heptane a long the dew point andbubble point l ines are given in Tables5 to 9 as a funct ionof pressure and temperature. The measurements have allbeen carried out a l i t t le above the saturation vap or pressurealong the differe nt isotherms. Th e values given in the tableswere obtained by applying an extrapolation technique along

each isotherm fitt ing a simple polynomial by least squares.Each isotherm is discontinuous at the saturation pressureexcept the supercritical isotherms. For pure n-pentane andn-heptane, a to ta l of 38 and, respectively, 50 experimentalpoints were measured in the range fro m 298K to th e criticaltemperatures. The dependenceof the viscosities o n temper-ature T for pure components are i l lustrated graphically inFig. 3.

The measurements were compared with the values ob-tained by o ther au thors [21, 241. The deviations are shownin Figs. 4 and 5. The measurements of Agaev and Golubev[24] are in excellent agreement with present results in theoverlapping range. At temperatu res fro m 298K t o T, for n-

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I. M. A bdulagatov an d S. M . Rasulov: Viscositv of N-Pentane. N-H eotane an d Their Mixtures 153

Table 8The viscosity of a 0 255 -pentane-0.745 n-heptane mixture along th edew point (q ) and bubble point ( q ' ) ines

T P P' v,.104 vfr.1o4 p ' P ,[K] [MPa] [MPa] [Pa.s] [Pa.s] [k g.m -3] [kg.m-3]

473483

493503508513517521523524525525 6526 2

1 2111 438

1 7081 9972 1552 3252 4902 6712 7562 7982 8402 8763 060

1 4801 709

1 9702 2682 4212 5802 7092 8472 9132 9492 9782 9973 060

0 78550 7110

0 63550 56300 52480 48570 45500 41450 39000 37650 35850 33700 2681

0.11000 1155

0 12670 14280 15300 16450 17550 19000 20360 21200 22650 23750 2681

461 6443 9

420 2392 3377 8359 5331 0317 5301 5290 0277 0269 5234 4

39 048 1

60 075 .o84 596 8

112 5134 6149 0158 0167 8173 5234 4

Table 9The viscosity of n-heptane in the liquid( q ' ) and vapour ( q ) phases

along the saturation line

T P vf.103 v f .l o p ' P"[ K] [MPa] [Pa . s ] [Pa . s] [kg .m-3] [kg .m-3]

298 0 006 0 3879 - 679 3 0 25313 0 012 0 3368 - 666 5 0 50333 0 028 0 2799 - 649 1 1.10353 0 056 0 2377 - 631 1 2 00373 0 105 0 1967 0 0073 612 4 3 60393 0 181 0 1660 0 0078 592 6 6 08413 0 294 0 1420 0 0083 571 1 9 79433 0 454 0 1208 0 0089 548 1 15 1453 0 669 0 1017 0 0097 523 2 22 4473 0 959 0 0864 0 0105 495 2 33 0483 1 136 0 0794 0 0112 479 3 40 1493 1 337 0 0723 0.0118 461 6 48 9503 1 566 0 0650 0 0127 441 4 60 0513 1 825 0 0583 0 0136 417 7 74 5518 1 964 0 0548 0 0145 404 6 83 6523 2 111 0 0518 0 0153 387 7 94 6527 2 239 0 0494 0 0161 375 0 105 0529 2 303 0 0479 0 0166 366 4 111 7531 2 366 0 0462 0 0172 357 4 119 1533 2 433 0 0443 0 0177 345 7 128 7535 2 504 0 0422 0 0187 333 2 139 7537 2 569 0 0394 0 0200 316 6 153 8538 2 618 0 0375 0 0215 305 9 163 1539 2 661 0 0357 0 0231 290 7 177 8539 6 2 685 0 0344 0 0248 281 9 189 5540 1 2 701 0 0269 0 0269 235 0 235 0

pentane and n-heptane their results deviate from ours byless than ko .5 . Only for a few experimental points thedeviation reach f 1Vo.

For liquid n-pentane along the saturation line, the dif-ferences between our new viscosity measurements obtainedwith the capillary-flow method and those obtained byKhalilov [21] with the sam e method at temperatures f rom353 K t o 423 K are less than k 1 , however, a t temperaturelower than 353 K the differences reach +6 . For liquid n-heptane , the differences between our results and Khalilov's

eJ

1.8 1

0 6

0.0

n pentane

.

.

-0.6 I I l l r ~ r l r l l l l l l . I I l I , I I I I , , , , ' ,270 320 370 420 470

Te m pera tu re /KFig. 4Relative deviations of the measured viscosity of n-pentane from theAgaev and Golubev [24] data. in the vapor phase; - in th e li-

quid phase

1.5 If In heptane .

.i

290 340 390 440 490 540

Temperature/K

Fig. 5

Relative deviations of the measured viscosity of n-heptane from theAgaev and Golubev [24] data. in the vapor phase; in the li-quid phase

[21] measurements in the temperature range from313 K to493 K are less than k 0.7 . However, for the vapour phaseof n-he ptane the relative deviationsof the Khalilov's da ta[21] from the present results are very large (about 0 ).

There are no previous results of measurementsof theviscosity of n-pentane-n-heptane mixtures available.

4. Conclusions

New measurements of the viscosity of n-pentane and n-heptane along the saturation line and their mixtures at thedew point and bubble point l ines have been reported. Theresults show the behaviorof the viscosity of n-pentane, n-

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154 I . M. Abdulaga tov and S. M. Rasulov: Viscosity of N-Pentane, N-Heptane and Their Mixtures

heptane a nd their mixtures over wide rangesof temperature [20] H.H. Remer, G.M . Coklet, and B. H. Sage, Analit. Chem. 31an d pressure, including the crit ical region. The accuracyof 1422 (1959).

[21] Kh.M. Khalilov, JETP 9, 335 (1939) (in Russian).[22] A.Z. Golik, 1.1. Adamenko, A.A . Tkachenko, and A.R. Zelen-

the viscosity da ta is estimatedto be I . 2 .

chuk, Ukr. Phys. J. 21, 53 (1976).The research was supported by the Russian Science Foundation [23] P.W. Bridgman, Proc. Amer. Acad. 61 57 (1926).

[24] N.A. Agaev and I.F. Golubev, Gazovay promyshlennost 8 , 45

[25] N.A. Agaev and I.F. Golubev, Gazovay promyshlennost 3 50

under Grant 93-05-8627.(1963).

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(1949).

.

I .F. Golubev, Viscosity of Gases and G as Mixtures, p . 84, IsraelProgram for Scientific Translations, Jerusalem, 1970.B.A. Grigorev, D. S. Kurumov, I.M. Abdulagatov, and Ya. L.Vasilev, Teplofizika Vyasokikh Temperat ure 24, 1096 1 986).A.F. Collings and E.McLaughlin, Trans. Faraday SOC. 67 340(197 ) .D. W. Brazier and G. R. Freeman, Ca n. J. Chem. 4 7 , 893 (1969).A. A. Tarzimanov, V. E. Lyusternik, and V.A. Arslanov, Vayz-kost gazoobraznykh uglevodorodov, Moskow. IVTAN 1987.J. S. McCoubrey and N. M. Singh, J. Phys. Chem. 63 517 (1963).M. Diaz Pena and J.A . R. Cheda, An. Quim. Real. SOC. Esp. fis.yquem. 71 34 (1975).

M. Diaz Pena and J . A. R. Cheda, An . Quim. Real. SOC. Esp. fis.yquem. 70 107 (1974).L.T.Carmichael and B. H. Sage, J. Amer. Inst. Chem. Eng. 12,559 (1966).I.D. Lambert, K . I . Cotton, M.W. Pailthorpe, Proc. R. SOC.A232 280 (1955).R.M. Melaven and E.Y. Mack, J. Amer. Chem. SOC. 4, 888(1932).D. S. Kurumov, Teplofizika Vyasokikh Temperature 28, 1107(1990).J. V. Sengers, in: Transport Phenomena 1973, p . 229, ed. byJ. Kestin, ASP Conf. Proc. 11, 1973.G. A. Olchowy and J .V . Sengers, Phys. Rev. Lett. 61, 15 (1988).L. W.T. Gummings, F. W. Stones, and M .A. Volante, Ind. Eng.Chem. 25, 728 (1933).

R.M. Habbard and G . G . Brown, Ind. Eng. Chem. 35 1276 (Received: January 19, 1995( 1943). final version: Octobe r 13, 1995)

E 8879