Vapor Pressure of Water at Its Triple Point

The vapor pressure of water at its triple point was measured with exceptionally high accuracy by realizing it with a special apparatus and measuring the pressure with the NBS precision mercury manometer. The vapor pressure apparatus had a system for circulating the liquid water. Actual triple point conditions were established with a thin sheet of freshly distilled liquid flowing down over an exposed mantle of ice frozen on a vertical well. This technique reduced non-volatile contaminants and the vapor was repeatedly pumped to remove accumulated volatile contaminants. A diaphragm pressure transducer was used to separate the water vapor from the helium used to transmit the pressure to the manometer. The value found for the vapor pressure of water at its triple point was 611.657 Pa with an uncertainty of ± 0.010 Pa from random errors, computed at 99 percent confidence limits. The systematic errors are estimated to be insignificant relative to the random errors.


Introduction
W a ter is the stuff of life-th e working me dium for powe r ge ne r ation-the great hi ghway of comm er cethe d et erminin g fact or in the weathe r. It has s uc h importa nce to m a nkind th at probably no oth er sin gle co mpound h as received more atte ntion fro m the scie ntific world . Its pro perti es have been measured and r emeas ured ; the rm odynami c tables ha ve been construc ted a nd re peate dly re vi sed , a nd furth er work of this type is e ve n now commanding worldwide attention. In part, this kind of activity continues because water is not an e asy s ubstance to deal with. It is almost a universal solve nt , ofte n reacts with the materials of an expe rime nt , and is s usceptible to signific ant changes in its isotopic co mposition. Consequently, high accuracy in the measure ment of many of the properties of water is hard to achi e ve, a nd more effort is needed to exte nd or improve our knowle d ge of them.
It is our purpose to meas ure with the highe st possible accuracy th e vapor press ure of water for -5°C < t 68 < 100°C. W e chose to concentrate initially on th e vapor press ure of the triple point, which was known with poor accuracy. Alth ough a " triple point" is a precise designatio n for a phase diagram , it is not likely to be a n actu al point in its physical re alizati on. Th ermod yna mi cally, a triple point is a syste m containin g ma tter in three phases with each compone nt in e quilibrium throughout the syste m , i. e. , the che mic al pote ntial of each co mponentis the sa m e in e very ph ase.
If all three ph ases should happen to be in contact simultan eo usly (whic h is not a r e quire me nt of th e de finiti o n), the contact will be alon g a lin e produ cin g a closed c urve, r edu cin g to a point only .in th e limit. Furthe rmor e, th ere are se ve ral tri ple points of water. W e shall use th e unqualifie d expression , howe ver, to de note the e qu ality of the c he mical pote nti al of pure wate r in a syste m containing the three ph ases : ice I , liquid and vapor. Thi s is the o nly triple point of water involvin g the 3 states of matter and th e o ne of most importance. Not only is it the terminu s of th e ice 1va por press ure c urve and the begi nnin g of the e quilibrium liquid-va por press ure c urve,l but also its te mper ature, which can be expecte d to be invaria nt by the phase rule, has been assigne d a valu e that, in prin ciple, establishes all the rmodynamic te mperatures. This unique situation makes a highly a cc urate value of its vapor pressure, which is also invariant, e specially inte resting, because it can provide the foundation for exceptionally accurate th~rmodynamic calculations for water. This is true for this temperature region in particular because thermodynamic temperatures are inherently known with their highest accuracy in the region of the defining value.
Most values reported for the vapor pressure of th e triple point have been derived by interpolation or extrapolation of measureme nts of the two-ph ase e quilibria betwe en the liquid and va por as a fun ction I Also it is th e te rminu s of th e ice I-liq u id c urve, b ut th is is of no int e rest for va por pressure. measurements. of temperature. The most significant of these are the values of Thiesen and Scheel, 610.90 Pa [1],2 Scheel and Heuse, 610.90 Pa [2] and 610.55 Pa [3] and of Douslin, 612.1 Pa [4]. The average of the earlier results fitted along with data over a large temperature range is perhaps best represented, in the sense of a consensus, by the accepted value of the triple point in present day steam tables, viz., 611.2 Pa.
For equal accuracy of pressure measurements, those workers who actually realized the triple point probably attained greater accuracy in the measured vapor pressure. There are only two papers reporting such measurements: 1. The values of Prytz, published in 1931 [5], had an average of 4.5867 mm of Hg pressure, or 611.51 Pa.3 He realized the triple point statically, i.e., an incomplete layer of ice was formed on the surface of a quiescent pool of water. The pressure was measured by a mercury manometer using interference techniques to locate the me nisci with 0.5 J-tm Hg (0.065 Pa) imprecision, but the values of the vapor pressure varied by as much as 1.7 J-tm Hg (0.22 Pa). Prytz was of the opinion that the average value was about 2 J-tm Hg (0.26 Pa) too high.
2. L. Besley and G. Bottomley published two valu~s, 611.29 Pa obtained from direct measurement and 611.11 Pa derived by interpolation [6]. A special mercury manometer was used for the pressure measurements, with the height of the mercury column determined cathetometrically. The vapor pressure cell was connected directly with the manometer, as was also the case in the measurements by Prytz. Considerable effort was made to eliminate dissolved air in the filling of the cell. It was operated statically, being carefully thermostated to realize the 3-phase equilibrium at the surface of the liquid. The total uncertainty of either value was not given. The value derived from direct measurements was based on 148 determinations which varied between 4.579 and 4.590 Torr, and one might thereby regard the variation of ± 5.5 m Torr as equivalent to the imprecision at the 99.4 percent confidence level. The residual standard deviation for the polynomial, from which the interpolated value (4.5837 Torr) was derived, was 1.7 m Torr. The two imprecisions are not inconsistent, insofar as three residual standard deviations would approximate the imprecision of the interpolated value at the 99+ percent confidence level, except that in addition the uncertainty would be greater because the triple point was near the lower extreme of the range of the fit.
Our own method also realized the triple point, but in a dynamic system. Liquid water is distilled onto a mantle of ice and falls into a well to be pumped back to the still. This method helps to continuously reduce the concentration of dissolved gases which come out of solution in the still and in the pressure cell and are pumped off periodically. Since the evaporation from 2 Figures in brackets indicate the literature reference at the end of this paper. 3 Based on the equivalence of 760 mm Hg= 101325 Pa. the still is quiescent, nonvolatile impurities are retained in the boiler. To maintai!1 the purity of the water vapor in the triple point cell, and of the helium in the manometer line, the vapor pressure system is separated from the manometer line by a diaphragm pressure transducer.

Equipment
Improved accuracy of the measurements of the vapor pressure of water at the triple point can only be attained by: (1) Making more accurate pressure measurements. Realizing the triple point better. Improving the purity of the water, especially with regard to gases in solution. .
The measurements were undertaken in the NBS Gas Thermometry Laboratory because the first problem was essentially solved by using the NBS precision mercury manometer to measure the pressure. The second and third problems were dealt with by the con· struction of an elaboration of the triple point cell, and by the use of a metal diaphragm pressure transducer. The arrangement of the equipment is shown schematically in figure 1, where M is the manometer, D is the diaphragm, and the remainder is the valving and the triple point cell. We shall discuss the equip. ment in terms of these three main elements.

. The Manometer
Th e principles and many of th e details of the NBS precision mercury manometer are given in an earlier paper [7]. Essentially it is a W·tube manometer, with the locations of the crowns of very large menisci pre· cisely reproduced by the use of capacitance measure· ments, and with the height of the mercury column accurately measured by end length standards (gage blocks). The instrumentation of the manometer was designed so that a null signal on a capacitance bridge was observed when the gas pressure in the lower cells balanced the pressure from the mercury column plus the vapor pressure of the mercury in the upper cell. The maintenance of the pressure was made automatic by using the ou tput of the bridge to control a heater in a large ballast (a "thermal injector") so as to restore the pressure.
The pressure to be measured is between 611 and 612 Pa, corresponding to a height of the mercury column close to 4.6 mm. We bought a chromium carbide gage block of that length in the highest quality offered. It was carefully calibrated by J. S. Beers, Deputy Chief for Length in the Dimensional Technology Section. In figure 2 the interference pattern of this block indio cates very good flatness and parallelism, with one corner slightly low relative to the gaging point. These properties make meaningful the high precision of the calibration measurement, which had an estimated i:)tandard deviation of the mean of 2.6 X 10 -6 mm. This includes the variability due to wringing.
. Because it is impracticable to obtain a gage block of exactly the correct length (particularly in advance of knowing its value) some modification in our usual method of measuring pressure was necessary to pro· vide continuity over the interval between gage block lengths. There is too much uncertainty introduced by measuring an appreciable pressure difference directly by the diaphragm gage. However, the charac· teristics of the manometer cells are well known, so that an accurately known change of capacitance can be accurately related to a change of meniscus height. The bridge is balanced at "zero level" by adjustment of Cvan a 3·lead General Radio variable capacitor, Type 1422-CE,4 used in the range 0.005 to 0.11 pF, as shown 4Certain co mmerc ial materials and in st r.uments are identified in thi s paper in order to adequately s pecify the appa ratus and experimental procedure. Such identifica tion does not imply recommendation or endorsement by the National Bureau of Standards. . This capacitor has an imprecision of 0.0001 pF and was calibrated at the values used with an un· certainty of the reference estimated at ± 0.00003 pF. The uncertainties in the effective areas of the capac· itance plates (± 0.03% at 99% confidence) limit the attainable accuracy in calculating the change of menis· cus height from a change of Cvar . However, so long as the height of the mercury column differs from the gage block length by no more than 17 J-Lm, the contri· bution to the error in the measured vapor pressure from this cause will not exceed 1 ppm.

Modified Triple Point Cell
The vapor pressure apparatus, shown in figure 1, provided for circulation of the water. It was pumped from the pressure cell, PC, by a bubble pump, B into a reservoir, R. The reservoir was part of a still with a heater, H, to evaporate water into a condenser, C. The condenser water reentered PC at the top through a trap. The cell was 38 cm deep, with a volume of about 500 cm 3 • A thermometer well, W, 32 cm deep, was a close fit on the 7 mm diameter case of a platinum resistance thermometer. Seven bulges, 20 mm across , supported the ice mantle when the water was pumped out of the cell. The bubble pump was a vertical tube of 5 mm bore with a piece of perforated PTFE (poly tetrafluoroethylene), PT, inserted in the lower half. A 50· watt strip heater was taped to the tube and thermally insulated from the bath. The reservoir was 50 mm in diameter and had a volume of about 700 cm 3 . It had a reentrant tube HP, which extended to the top of the boiler. The tube contained C2C4F3 and functioned as a heat pipe, transferring heat from the heater, H, to the water surface. It was filled through the valve, V. There were three tubulations: one from the top of the cell to (e) (f) valve 4 was for the pressure measurements, and two others, P, one from the side of the cell and one from the condenser, were for pumping from the gas phase. The tubulations were sealed by PTFE gaskets to stainless steel high-vacuum valves at the top of the assembly.

Pressure Transducer
A special commercial pressure gage with a metal diaphragm, the position of which was sensed on one side by the capacitance between it and an electrode, was used as a null de vi ce to de tect equality of press ure be tween th e wa ter va por on th e one side a nd th e helium gas trans mittin g th e meas ured press ure on the oth er side. The null readin g co uld be determin ed before a nd afte r meas ure me nts by ope nin g the bypass, valve 2 in fi gure 1, and ad equately evac uatin g both sides.
Great care had to be ta ke n in the use of the in s trum e nt to achie ve th e needed stability, both electroni c and physical.

Filling of Vapor Pressure Apparatus
The vapor pressure app aratus was cleaned and filled by th e same tec hniqu es used in the pre paration of conve ntional triple-point cells . The glass was cleaned with chromic acid , rinsed , li ghtl y etc hed by h ydroflu ori c acid , and leac hed by s teaming. Two vapor press ure cells were filled in the course of a production run of triple point of water te mperature standards, with water that was purifi ed firs t by treatm ent with an ion exc hanger and th en quadruply distilled , with c he mical treatme nt for re moval of organi c mate rial be tween eac h di s tillation.
Samples of the purifi ed water were take n for isotopi c analysis at the time of fillin g and also later durin g operation_ Up to th e present , the re is no measure ment of the va por press ure of the triple point of naturally occ urring wate r for whi c h the maximum re ported vari ation of isotopi c composition would mak e a significant differe nce. Howe ver , the high acc uracy of th e prese nt meas ure me nts bein g re ported in thi s pa pe r require suc h a sp ecification to a void added uncertainty.

. Procedure
Th e operation of the equipm e nt co nsis ted of pre parin g the ma nome ter a nd the va por press ure a pparatus for meas ure me nts, determinin g the null of th e e vac uated diaphragm gage with the bypass valve ope n, and the n, after closing the bypass valve, bac k fillin g the diaphragm with helium on the s id e of th e cap acitor electrode and with water va por on the oth er. The vapor press ure appar at us was th e n vacuum pumped for 30 s in each of three s uccessive 2 min periods before an y actual meas urem ents were mad e. We shall expa nd on these prelimin aries and th e n describe th e meas ureme nts the mselves.
Th . manom e ter is " ze roed " with a fixed me rc uryto-capacita nce-plate se paration in the uppe r cell and for the corres pondin g se parations in the lower cells whe n all three merc ury me ni sci are on the same level. Und e r these conditi ons, th e " zero le vel" capacitance necessar y to bala nce th e ca pacita nce bridge (see fi g. 3e) is establis hed. Th e meas ure me nt of a vapor press ure consists of ge neratin g a nd meas urin g in the ma nometer th e e quivale nt press ure of helium , as e vid e nced by a zero press ure differe nce at th e di aphragm press ure tra ns ducer. T o do thi s, a gage block of appropri ate height is in serted betwee n th e uppe r cell a nd its pedes tal, a nd the press ure of helium in the lower cells and th e volum e of me rc ury in the manom-e te r are adju sted until all merc ury me ni sci are at a le vel relative to the capacitance plates to produce th e sam e capacitan ces as for zero level. In these meas ure me nts, for th e first time, we have modifi ed this procedure in ord er to interpolate be twee n th e gage bloc k valu es. W e adju sted th e manome ter press ure until the diaphragm was bala nced , a nd the n we balanced the manometer capacitan ce bridge by adju stin g evar.
The vapor press ure a pparatus whe n not in use is operated in a " Standby" mode, in whic h the wa ter is continuou sly circ ulated by pumpin g it out of the triple point cell into the still and di stilling it bac k into the triple point cell. Occasionally, the va por is vac uum pumped, th e purpose bein g to remove gases released from solution, Th e ope ra tin g para me ters, a nd e ve n som e de tail s of design , of thi s apparatu s wer e determined by lon g experim e ntation. The heat pipe in the co nde nser reser voir was necessary to a void overhe ating the wate r near th e bottom of the reservoir. With the a pparatus in a O°C thermostat and a heater power of 25 watts , the water tempe rature in the reservoir was about 25°C and nearly uniform up to 1 cm below th e s urface. Di stillation occurred at th e rate of about 0.01 g/s. Th e bubble pump, ope rated with a heater input of 15 W , initially tra nsfe rred a mixture of wate r a nd vapor from the full triple point cell to the reservoir at a rate of a bout 10 g/ min , but the rate dropped as th e water le vel dropped. Whe n th e cell was nearly empty, th e pump acted as a s till with a tra nsfer rate of a few g/ h.
T o prepare for meas ure me nts, th e a pparatu s was placed in a bath , the rmostated by circ ul a tin g liquid close to th e triple point te mpera ture a nd co nsta nt within 0. 2 mK. Th e va por press ure cell was filled b y di stilla tion from th e conde nser ( operated at 20 W thi s required a bout 24 h) _ Ba th fluid was circ ulated through the conde nser, a nd was pumped over th e top of th e cell and also onto th e ste m of a platinum resista nce th ermome ter in serted into th e well of th e va por press ure cell. (Whe n water was bein g pumped out of th e cell , a zon e at th e top of th e reservoir was cooled by pumping bath fluid over it also ) .
The a pparatus was re moved from th e b ath and a mantle of ice was froze n around th e th ermome ter well usin g powdered solid CO2 as the coolant. The completed mantle was from 5 mm to 10 mm thick.
The a pparatus was th en r eturned to th e bath, whic h was regulated at a te mpe ra ture not more than 1 mK below the triple point te mper ature a nd the bubble pump was started. By th e next morning, the cell was nearly e mpty wher e upon th e reservoir heate r was turn ed on. It distilled wate r into th e press ure cell at a bout 0.01 g/s (with the bubble pump left on, meas ureme nts co uld be co nducted for se veral hours before e nough water acc umulate d in the cell to touc h the ice mantle).
In the meantim e, both sides of the diaphragm gage had bee n e vac uated ove rni ght with an ion pump. A " zero" reading was obtain ed with the gage isolated and the bypass valve open. Then the bypass valve was closed, the electrode side of the diaphragm cell was filled with helium, and the other with water vapor (with the differential pressure aCf(?SS the gage kept within ±1 mm Hg). Finally, adjustments of the manometer variable capacitor were made in order to balance its bridge when the manometer pressure was such that the reading on the diaphragm gage was very near the "zero" value.
Next, to sweep out gaseous impurities, the water vapor was pumped from the pressure cell, at a rate of approximately 100 cm 3 /s (0.6 cm 3 S.T.P./s). When the apparatus was in regular use, an initial set of three pumpings, each pumping lasting 30 s over a period of 6 min was sufficient to insure no effect after recovery to a steady state would be observed with further pumping.
Chart records were made of the diaphragm gage output for its zero, and immediately following the last pumpout, readings of the output of the diaphragm gage were recorded. Because the stirring of the thermostat had to be stopped to avoid shaking the diaphragm, th~ recordings were made for 20 s periods every two minutes. After each set of 3 recordings, the water vapor was again pumped for 30 s. After 4 such sets, the apparatus was closed off, the diaphragm bypass valve opened, and the diaphragm pumped out for 20 min when a new "zero" was recorded. During each measurement, the temperature of the diaphragm was sensed by reading the e.m.f. of a copper-constantan thermocouple referred to ice.

s. Measurements
Besides general experimentation to establish effective operating techniques, there were three periods of several weeks during which actual pressure determinations were made. The first period was purely instructive and resulted in vigorous efforts to improve various aspects of the equipment, in particular the diaphragm gage. The results of the second period reflected substantial improvement in the accuracy of the measurements, and were reported at the 1974 meeting of the International Association for the Properties of Steam in Giens, France [8]. The results of the third period are decidedly more accurate than the second, more because of further improvement in the diaphragm gage than anything else. However, numerous possible effects were investigated in addition, and these results will be described here before presenting the final sets of measurements.
Three standard calibrated platinum resistance thermometers were used to measure temperature, one in the well of the vapor pressure cell, the second to measure the temperature of the thermostat bath close to the vapor pressure cell, and the third as a regulator sensor. They were calibrated in a triple point of water cell each day; it is believed the values of the measured temberatures were uncertain by no more than 30 ILK. The temperature registered by the thermometer in the well of the vapor pressure cell could be used as an indication of the state of the mantle. When the ice mantle was dry or nearly so, pumping resulted in a rapid reduction in the pressure, by about 100 Pa, and in the temperature, by about 0.1 K. When an adequate flow of water was maintained over the ice during pumpout, the drop in pressure was no more than 0.5 Pa and in temperature no more than 0.1 mK.
It has also been observed during a run earlier than any being reported that when air in an amount> 100 mm Hg in pressure had entered the cell, the temperature at the mantle was depressed by several tenths of a mK and did not recover fully before a new mantle was frozen.
The effects on the observed vapor pressure resulting from variation of the bath temperature from the temperature of the triple point were studied. For temperatures in the range from 1 mK below the temperature of the triple point to 200 mK above it, scarcely any variation of the vapor pressure was observed. This indicaJed that the temperature surrounding the apparatus was not very critical, and furthermore, there was probably no undesirable effect from the warmer parts of the tubulations which extended out of the bath. In the final measurements, the bath was thermostated at, or not more than 1 mK above, the temperature of the triple point of water.
The diaphragm unit itself was not thermostated, but was thermally lagged with a thick layer of insulation. Its temperature was measured at frequent intervals, and in its final physical and electronic configuration, a consistent relationship between the copperconstantan e.m.f. 's and the zero readings existed. A straight line was fitted to the data by the method of least squares with the result that the zero can be calculated from the e.m.f. by the following equation: y= 893.627 -0.748503 V where y is the chart reading for the diaphragm zero and V is the thermocouple e.m.f. in IL V. The residual standard deviation was 1 chart division, and the standard deviation of it predicted point was about 0.5 chart division. This equation was used to calculate the chart zero pertinent to any given chart pressure reading, from thermocouple e.m.f.'s observed at the same time.
No effect dependent on refreezing the mantle was observed, and in fact, so long as crystals of ice remained, it appeared that the pressure was established, except for the change in the "pressure head", i.e., the pressure due to the weight of the column of vapor above the effective location of the line at which triplepoint conditions exist. 5 The values given in this paper were measured on four successive days and consist of the following five "sets" : A group comprises the values measured between pumpouts. After the in itial three 30 s pumpouts, the apparatus was pumped about every 10 min. At the conclusion of all the measurements, the value of the capacitance to balance the capacitance bridge for the manometer at zero level was redetermined.

. Equations and Calculations
Because of the effect of the pressure head, there is only a surface, a horizontal plane except for temperature perturbations, at which the triple point press~re can exist. T he pressure of the water vapor at the lme formed by the intersection of the surface with the mantle is given by the following: where ex is 1. ( av ) for mercury, p is the density of V at P mercury under zero pressure at 20°C, g is the acceleration due to gravity, the 8t's are differences of temperature from 20°C of the upper cell (UC), the average of the lower cells (LC), and the mercury arm (Hg). The height of mercury in all the cells is substantially the same and is symbolized by huc for the upper cell or by fi LC as the average for the lower cells. The height of the mercury column is h 2 , and the pressure head is produced by the height of the gas column between the menisci of the lower cells and the center of the diaphragm (which was mounted ver· tically), designated ho. The pressure head depends upon the molecular weight M. The numbers are consistent for values of the symbolic quantities in S.1. "Manometer readings," comprising the observ(~: tions of the resistance of a capsule platinum resistance . thermometer located in a thermocouple reference block and the e.m.f.'s of all 4 sets of differential thermocouples for the upper cell, the mercury arm, the left lower cell and the right lower cell, were made once or twice for each set of vapor pressure measurements. The temperatures of the vertical com ponents of the mercury lines were calculated from the thermocouple e.m.f.'s as a difference from the temperature of the reference block. There were twelve copperconstantan thermocouples in series fastened to the upper cell, twenty· five to the mercury arm, ten to the left lower cell and twelve to the right lower cell. The observed e.m.f.'s were converted to temperature differences by a "handbook" sensitivity of 40.  (table 1) were obtained when the expenmental data were calculated by the program PRSURE, given in appendix II.
The manometer zero was established from 10 determinations made over a period of 10 days. The values  The estimate of the standard deviation of the mean is 5 = 0.00012 pF.
8P Wring is the net correction for imperfectly joined gaging surfaces between the wringing boss on the bottom of each cell and the pedestal or the gage block. The leak rate through the gap formed when two gaging surfaces meet on one edge with a dihedral angle cf> (in p. rad) was studied [10] and is given for the particular blocks and volume of vacuum system as dp/dt = 0.42 cf> 2 + 0.022 cf>3 p.m Hg/min. The rates were remeasured after every adjustment of any cell position. The net press ure effect is given in the following: 8P evar is derived from th e chan ge of mer c ury level r equiring a change of the variable capacitor to maintain the manometer bridge balance. The chan ge of level can be accurately de te rmined because of the coaxial switching arran ge m e nt that is part of th e manometer instrumentation. Th e configurations used are shown in figure 3. Th e manometer tran sform er has two taps on the right-hand side, and one on the left.
The tap RI has 3/4 the voltage of L, and R2 has the same voltage as L. Th e variable capacitor may be switched to any tap.
There is also a switch which changes ground from the center tap to the other side of the detector. There are 3 standard capacitors, labeled Ch Cn. and Cm. The value s of C 1 and C n are 8.2046 ± 0.0008 pF, and are eq ual within 1 ppm. Th e value of CIII is 3.0503 pF, so that it can be used to m eas ure th e lower cell capacitances. The capacitan ces of the variou s parts of the de tection system and the manom eter we re found from th e followin g sets of meas ure m e nts at zer o le vel:

Ll~C LR = 47T
A LCL So(LCL) + d -So (LCL) The pressure in pascals is related to the displacement in /Lm as P Cvar = 0.132763 X d Pa.
a The num ber of di gi ts is consistent with the imprecision. The total The values obtained are given in table 6.
uncertainty is nearl y I part in 10 4 , but the net changes are kn own within 3 ppm of the total figure. 8PThermp, the effect of thermomolecular pressure, is expected to be significant only in the pressure transmitting tube of the manometer. This tube, which is 0.l512 cm in radius, ran from the manometer vault, at a temperature very close to 20 °e, to the valves that were physically adjacent to, and assumed to be at the temperature of, the diaphragm unit.
The value of the effect was derived from the equa-  8PDIA , the pressure difference at the diaphragm, was derived from sets of charts readings. Following the stated operating procedures, we recorded the diaphragm zero and the copper-constantan thermocouple reading, then pumped three times, after which three sets of measurements, each set consisting of a thermocouple reading and a diaphragm reading for the pressure difference, were recorded. The diaphragm output was recorded for 20 severy 2 min. The thermocouple was read again while the water vapor was repumped from the vapor pressure cell. Three more thermocouple and pressure readings were taken for 20 s at 2 min intervals, and then the diaphragm was evacuated for 20 min and a diaphragm zero recorded. It was experimentally demonstrated that this period of evac uation of the diaphragm was long e nough to assure reliable zero values.

RK Tl + T2 '
where g is the acceleration due to gravity, M is the molecular weight of the vapor, R is the molar gas constant, K is the conversion factor between units of pressure, hJ is 0.244 m running between the diaphragm at 25°e and the bath at 0 °e, and h2 is the distance, 0.07 m, in the bath at O°c. Then 8PVa PHd = 23.31 X 10-6 PMan = 0.01424 Pa.
The average temperature, T1 , was weighted on the high side. The value is bounded by the extremes, of course, and within those limits any reasonable choice would hardly make any significant difference in the final pressure.

Results
The results are summarized by totalling the elements of pressure for each set (all values in pascals): The ave rage of the 5 sets is 611.6571 Pa (S = 3.94 mPa). The estimate of the standard deviation of the mea n is S", = 1. 76 mPa.

Isotopic Composition
The determination of the isotopic content of samples from the vapor pressure cell relative to SMOW (standard mean ocean water) depended upon two steps. First, the isotopic content of cell water was determined relative to NBS-l standard water [12], the composition of which had, as a second step, been related to SMOW by the work of Craig [13]. The D/H absolute abundance ratio of SMOW has been determined very precisely by Hagemann, Nief and Roth as 155.5 ppm [15] . The value for the absolute abundance of 0 18 in SMOW is based on Craig's measurements [13,14] and as variously interpreted may be taken to be 0 18 /0 16 = 1993.4 X 10-6 to 1995 X 10-6 , of which the latter is used here. The compositions of seven samples of the water used in the vapor pressure cell, both relative to SMOW and absolute, are as follows: Di still ed from apparatus 2 weeks after -6.

1982
All measurements were made with the second cell. The difference between the vapor pressure of the cell water and SMOW because of the reduced compositions of D and 0 18 can be calculated from measurements of Majoub [16], who reported that the ratio of PHDO/PH20 at DoC is 0.8994, and of various authors [16,17,18], who reported ratios of P H20'8/ P H20 .6 at 0 °C that average about 0.9885. The difference of pressure may then be derived from Raoult's Law, where the pressure of the liquid of the sample at 0.01 °C is 1 ppm more than the corresponding m«:!tastable SMOW. The sample triple point temperature is about 40 ILK lower than the triple point of SMOW [19]. Given that dP/dt is about 44.4 Pa/K for water at 0.01 °C, the effect of the differ ence in temperature of the triple points is about 3 ppm. Thus the vapor pressure at the triple point of the sample, whic h corresponds closely to the analyses of typical "continental water," can be calculated to be about 2 ppm , or 1.2 m Pa, less than the vapor pressure at the triple point of SMOW.

. Discussion
It is, of course, crucial to the reliability of any data that procedures be established to eliminate or satisfactorily minimize possible errors before any final measurements are made. We believe that the probable difficulties requiring special study were (1) the possible variation of the vapor pressure because of a slow return to equilibrium following a pumpout, or with variation of ambient temperature, (2) the presence of contaminating gas in the system, and (3) the possible errors in determining the diaphragm zero. Each of these problems received special study.
As discussed in section 5, the pressure and te mperature were only slightly perturbed by pumpout so long as all three phases were maintained about the mantle. Similarly, in the presence of the mantle, there was at most only a slight c hange in vapor pressure when the ambient te mperature varied from 1 mK below to 0.2 K above the triple point. Thus the actual realization of the triple point must have contributed great stability to the vapor pressure; the broad expanses of exposed liquid and solid phases could be expected to fulfill the physical necessities for facilitating such an equilibrium.
The procedure of pumping for three 30 s intervals prior to measurements, and subsequently for 30 s every 10 min was adopted because the measured pressure, with lesser amount or frequency of pumping, varied in a way to indicate the accumulation of measurable amounts of contaminating gases. The three recorded diaphragm pressure readings made in each interval between pumping showed no evidence of preferential drift that might indicate the rate of pressure buildup to be significant in that span of time.
An accurate measurement of the diaphragm zero depended upon the evacuation of enough of the sorbed gases (particularly water vapor) that the remainder would not exert a significant pressure difference between the two sides of the diaphragm, with the by-pass valve open. It was observed experimentally that a 20 min evacuation following pressure measurement appeared to be sufficient. These measurements together with the thermocouplee.m.f. 's observed at the same time correlated with those values of zeroes after long pumping and their concomitant thermocouple e.m.f. 'so This fact offered substantial confirmation both that 20 min was an adequate pumpout and that the diaphragm zero could be accurately associated with the thermocouple readings. However, measurements made when the room temperature varied rapidly were not in agreement with the rest of the results, and were not used. The assumption was that the thermocouple, being on the outside of the diaphragm, could not have represented the appropri-ate temperature when there were substantial gradients.
The reader may note that the corrections for C Var appear to be inconsistent. This is because a different reference line for reading was used at different times.

Estimation of the Total Uncertainty
The stated total uncertainty consists of the limits, at 99 percent confidence level for the random errors; and the systematic errors, estimated conservatively enough to warrant about the same confidence level.
The estimates of the values of the errors are expressed initially as one standard deviation. It is useful to treat them in two groups: (A) Those sources of error which contribute to the imprecision calculated from table 9, and (B) those additional sources of error which have a fixed effect on the directly determined value.
The term "systematic error" can be understood, and is used by some authors, to denote any error that introduces a constant bias into the observed results. For example, this is true of each of the items of Part B. However, in all but the last entry the errors were evaluated from well-defined imprecisions, and do not . differ in their nature from the imprecisions in Part A. These imprecisions are combined in a sum of the squares addition with those of Part A. In a more restricted definition, we are referring to systematic errors as those which introduce a bias into the results but which are not well enough investigated to be evaluated by statistical techniques, or are not realized to be important. The limits of a systematic error are apt to be less well-defined than for a random error, although there must be some theoretical or experimental results upon which an estimate can be based. The sum of the random errors in Part B , combined by the square root of the sum of the squares, is 0.0018 Pa. There is also a systematic error of 0.0003 Pa.
We attributed an element of syste matic error to the las t e ntry in Part B, in asm uc h a neith er theory nor ex pe riment for th ermomolec ular pressure eff~c t s is co mplete. Another important syste ma tic error mi ght be th e effect of con tamin a tin g gases on th e measured pressure. We be]jeve our eq uipm e nt and procedures were devi sed in s uc h a way that we were able to prove that thi s error co uld not have been significant in our meas ure ments.
The combination of th e various random errors for 99 percent confiden ce ]jmits re quires that they be weighted differently according to th e number of degr ees of freedom . Th e random errors in Part A were applicable to the 5 fin al pressures of table 9. With 4 degrees of freedom, th e standard deviations were multiplied by 4.6 as give n in Student's Table [20], to com pute th e limits for 99 percent confide nce.
In Part B , the number of degrees of freedom is nine or more, so that a multiplier of 3.2 was used. The separate weighted standard deviations of Part A and Part B were co mbin ed by the s um of th e squares, to gi ve an estim ated uncertainty of ± 10 mPa a t the 99 percent co nfide nce limits. The total addition al syste mati c errors are estimated to be relatively in signifi can t. .