The fourth interlaboratory comparison of 10 V

metrologia

The fourth interlaboratory comparison of 10 V Josephson voltage standards in North America C. M . Wang and C. A. Hamilton

Abstract. An interlab oratory com parison of Josephson voltage standards has been m ade among ® fteen national, industrial, and military standards laboratories in North America. The comparison was made at 10 V using a set of four travelling Zener referen ce stand ards. The uncertainty ( ) of the com parison is estim ated to be 17 parts in . The measurem ents of all participants fall with in this uncertainty, indicating that no signi® cant differen ce has been detected among them .

1. Introductio n In the 1997 Josephson voltage standard (JV S) interlab oratory comparison (IL C), a travelling set of four 10 V Zener referen ce standards was circulated among the ® fteen particip ating standards laboratories listed in Table 1. All of the laboratories used 10 V Josephson stand ards to measure the output voltage of the four stand ards. The m easurem ents were m ade between January and May 1997. A com parison of the measurem ents of all laboratories yield s data on the uncertain ty of each laboratory’ s m easurem ent procedure, the performance of the travelling standards, and any offsets that m ay exist betw een the referen ce and testing laboratories. Tab le 1. Participants in the 1997 JVS ILC. Lockheed M artin Astronautics, Denver, CO Fluke Corporation, E verett, WA Hew lett-Packard, Loveland, CO Navy M id-A tlantic Regional Calibration Center, Norfolk, VA NA SA K ennedy Space Center National Research Council, Ottawa, Canada Naval Aviation D epot, San Diego, CA NIST , Boulder, CO NIST , Gaithersburg, M D Sandia N ational Laboratory (SNL ), Albuquerque, NM US A rmy P rimary Standards Laboratory, Redstone A rsenal, A L Lockheed M artin M issiles and S pace, Sunnyvale, CA NWAD Corona, CA Hypres, Inc., Elmsford, N Y Air Force P rimary Std. Lab., Heath, O H

C. M . Wang and C. A. Ham ilton. National Institute of S tandards and Technology, Boulder, Colorado 80303, U SA. C. M . Wang is a m athematical statistician in the Statistical E ngineering D ivision. C. A. H amilton is an electrical engineer in the E lectromagnetic Technology Division. M etrologia, 1998, 35, 33-40

Commercial Zener dc reference stand ards were used in the com parison . These stand ards use batteries to m aintain the Zener tem perature and bias curren t for at least 48 hours witho ut ac power. Next-day deliv ery airfreig ht was used for all shipm ents. Only once in the sixteen shipm ents did the deliv ery take tw o days. None of the four Zeners suffered battery failure during the course of the IL C. 2. M easurem ent procedure After waiting at least one day to charge the batteries and stabilize the internal tem perature, each laboratory made approxim ately sixteen measurem ents of each of the four Zener standards over a perio d of 2 to 6 days. A measurem ent typically results from averaging the differen ce voltage between the Josephson standard and the Zener referen ce over several m inutes and tw o or more reversals [1]. These reversals are made either with an automated scanner or a manual reversing switch. In order to guard against unreversed therm al emfs in the switches or the wires, the connection s at the Zener term inals were physically reversed after every second measurem ent. Since ground-loop noise coupled through the Zener power supply interfe res with some Josephson stand ards, all measurem ents were m ade with the Zeners on battery power. Line power was rem oved im mediately before recording a measurem ent set and restored im mediately after, in order to duplicate the battery charge history (and therefo re the intern al Zener tem peratu re) as nearly as possible at each laboratory. In some previous JVS interlab oratory comparisons [2, 3] one laboratory has served as a pivot with the travelling stand ards returning to the pivot after each set of m easurem ents by a satellite laboratory. This is a major effort and in 1997 no laboratory volunteered to act as the pivot laboratory. Thus, in this IL C, 33

C. M. Wang and C. A. Hamilton

the standards travelled from one laboratory to the next until all ® fteen laboratories had participated. One laboratory (NIST, Boulder) contribu ted three sets of measurem ents, near the beginning, middle, and end of the ILC. The measurem ents for SNL and NASA were intersp ersed during the sam e week using an SNL laboratory JVS and a newly designed, NASA-ow ned, portable JVS [4]. With out a pivot laboratory there is a question about what the ª correctº value of the stand ards is. This question is further com plicated by the fact that the Zener stand ards drift with tim e, and their voltage has a sm all and unknown dependence on tem peratu re, pressu re, and humidity. A pivot laboratory allows the drift with tim e of the stand ard to be determ ined. We can deal with this problem by assum ing that the Zener reference voltage is described by the m odel (1) where is a constant, is the tim e in days from a reference start date, is the laboratory pressu re, is the laboratory tem peratu re, is the laboratory humidity, and is the random noise. In this IL C, however, both tem peratu re and humidity are left out of this model because the tem peratu re data are incomplete and the humidity effect is believed to have a tim e constant (at least several weeks) that is longer than the tim e spent in each laboratory. Resid ual humidity effects will contribute to the deviation of indiv idual laboratory results from the linear ® t. In addition, we use the laboratory pressure data converted from the laboratory altitu de data in model (1). Values for the constants , , and are obtained by doing a least sum of squares (LSS) ® t of (1) to the data from all participants. Possible differen ces between laboratories are estim ated using the residuals from the ® tted line of (1). The residual is de® ned as the differen ce between the m easured value and the ® tted lin e of (1). W hile we believe that this is the best approach for this Josephson IL C, there is a danger because the referen ce voltage is determ ined by everyone’ s data, including data that might be in error. Some possib le consequences of this approach can be seen in the exaggerated hypothetical exam ple of Table 2. Here we assum e that on successiv e days, nine out of ten laboratories m ake a perfect measurem ent of a 1 V standard while one of them (L aboratory E) is in erro r by 1 % . If we use (1) (w ith only) to determ ine the reference voltage of the standard then the estim ated erro r (residual) of each participant is show n in column 4. If the 1 % error had been m ade by Laboratory A, then the estim ated errors change as show n in columns 5 and 6. Thus, an erro r by any particip ant affects everyone’ s estim ated erro r and the magnitu de of the effect for any laboratory depends on its positio n in the tim e sequence relativ e to the offend ing laboratory. Therefore, a necessary condition for the validity of the com parison in this approach is 34

Table 2. M easurements and residuals of a hypothetical exam ple (residuals computed using LSS). Lab. Day

M easured voltage

Residual/V

M easured/V

Residual/V

A B C D E F G H I J

1 1 1 1 1.01 1 1 1 1 1

±0.0013 ±0.0012 ±0.0012 ±0.0011 0.0090 ±0.0010 ±0.0009 ±0.0008 ±0.0008 ±0.0007

1.01 1 1 1 1 1 1 1 1 1

0.0065 ±0.0029 ±0.0024 ±0.0018 ±0.0013 ±0.0007 ±0.0002 0.0004 0.0009 0.0015

1 2 3 4 5 6 7 8 9 10

that there should not be any outly ing points or that some method be adopted to m inim ize the effect of outly ing points. Because of this possible problem with outliers we also use a robust regression procedure, least m edian of squares (LMS) [5], to valid ate the LSS ® t. Instead of minim izing the sum of squares of the residuals as in the m ethod of the LSS, an LMS ® t is obtained by minim izing the median of the squares of the residu als. The m edian is not affected by the values of the outly ing residu als and indeed will not change unless m ore than half the residu als represent bad or spuriou s data. Another useful featu re of LMS is the exact ® t property. If at least half of the observatio ns exactly follow the lin ear relatio nship appearing in (1), then the LMS solutio n produces the correct equation . For exam ple, in the exaggerated exam ple of Table 2, the LMS ® t would produce a residu al of 0.01 V for Laboratory E and 0 V for the rest of the laboratories, and sim ilarly, a residual of 0.01 V for Laboratory A and 0 V for others. Figure 1 illu strates the robustn ess

Figure 1. Robustness of the LMS ® t. The LSS and the LMS ® ts are denoted by the solid and the dashed lines, respectively. M etrologia, 1998, 35, 33-40

The fourth interlaboratory comparison of 10 V Josephson voltage standards in North America

of the LMS techn ique with respect to outliers. Lines ® tted by both LSS (solid line) and LMS (dashed lin e) are show n when there are seven data points with tw o aberran t values. The effect of the outliers on the quality of the LSS ® t is obvious, while the bene® t of the LMS criterio n is equally apparent. Evidently , LMS is a majority-rules procedure; it ® nds a ® t to the majority of the sam ple and detects an exact ® t of the majority of points if such a subset exists. In any case, the basic properties of the LMS ® t show that it is not only a highly robust estim ation techn ique, but also an excellent tool for identifyin g multip le outliers. 3. M ain results 3.1 The model We ® rst present the measurem ents from all laboratories in Figure 2. The horizo ntal and vertical axes are the tim e in days from 27 Decem ber 1996 and the deviation (in nanovolts) from 10 V of the m easured voltages. The symbols , , +, and are for stand ards 1, 2, 3, and 4, respectively. The basic statistica l m odel we use

to describe voltage measurem ents may be written as (2) where represents the -th m easured voltage (deviation from 10 V in nanovolts) for the -th stand ard of the -th laboratory, is the elapsed tim e (in days), and is the laboratory pressure (in kilop ascals). In addition, , , and , where is the number of m easurem ents taken by laboratory for standard . The quantity is the residu al that cannot be accounted for by the regression line. Two possib le sources of this deviation are the laboratory effect and the random noise. In other words, each measurem ent can be thought of as an overall average (rep resented by a regression line) plus a laboratory bias plus a random erro r or other (such as residu al humidity). M odel (2) assum es that the drift rate , and the pressu re effect , are differen t among the four standards. Possible differenc es between laboratories are detected by com paring the laboratory effect with the random noise. If the laboratory effect is not signi® cantly larger than the random noise, the laboratory differenc es

Figure 2. Voltage m easurements of all participants. The horizontal and vertical axes are, respectively, the time in days from 27 D ecember 1996 and the deviation from 10 V (in nanovolts) of the m easured voltage. The symbols , , +, and are for standards 1, 2, 3, and 4, respectively. M etrologia, 1998, 35, 33-40

35


may be attribu ted to m easurem ent noise and the random ¯ uctuations of the standards them selves. Both the laboratory effect and the random noise are estim ated from the residu als to the ® t in (2).

Table 3. LSS regression coef® cients of (2) for each standard. Standard

Q uantity

3.2 Results for each standard

1

( 0 V )/nV 1 (nV/day) 2 (nV/kPa)

2

We ® rst perform the LSS ® t of (2) for each stand ard and use the residuals from the ® t to estim ate the laboratory effect (the betw een-laborato ry variatio n) and the random noise (the with in-labo ratory variatio n). The results of the ® ts are given in Table 3. Colum ns 3 and 4 of Table 3 contain the regression coef® cients and their standard uncertain ties. The t-value (w ith 293 degrees of freedom) is the ratio of the regression coef® cient to its standard uncertain ty and is used to test the signi® cance of the corresp onding effect. It appears that both tim e and pressu re are very (statistic ally) signi® cant. Both the tim e and pressu re coef® cients vary substantially among these four stand ards and should not be taken as representative of this type of standard. We are aware of stand ards of the sam e make and model with tim e or pressu re coef® cients that vary by as much as an order of m agnitude from the values listed in Table 3. Table 4 contains the results of ® ttin g (2) using the LMS procedure. We only give values of regression

Standard uncertainty

t-value

9148.66 49.96 ±11.93

121.20 0.28 1.29

75.5 177.1 ±9.3


6203.84 37.77 ±28.77

100.43 0.23 1.07

61.8 163.1 ±27.0

3


10 130.48 52.83 ±16.14

166.33 0.38 1.76

60.9 137.7 ±9.1

4


3051.82 43.15 ±14.65

117.87 0.27 1.25

25.9 158.7 ±11.7

coef® cients and do not provide for other statistics due to the com plicated distribu tional properties of the LMS estim ators. Relative to the standard uncertain ty of Table 3, these tw o ® ts seem somewhat different. However, when we exam ine the residu als from both ® ts, they are com parable. Figure 3 plots the LSS ( ) and the LMS ( ) residuals of each laboratory for stand ard 3. The pattern and the range of these tw o residuals indicate that these tw o ® ts are very sim ilar. Consequently , it

Figure 3. Residual plot for standard 3. The LSS residuals are denoted by

36

Value

and the LMS residuals by

.

M etrologia, 1998, 35, 33-40


Tab le 4. LMS regression coef® cients of (2) for each standard. Standard

( 0

1 2 3 4

8556.8 6704.4 9917.0 2558.6

V)/nV

1 (nV/day)

2 (nV/kPa)

50.47 37.16 55.50 42.96

±5.36 ±33.57 ±16.38 ±8.86

appears that there are no extrem e ª in¯ uentialº points in the data. Again, we should emphasize that the LMS ® t is prim arily used here as a tool for identifyin g m ultiple outliers. Let be the residu al of the ® t. is an estim ate of . The random noise, characterized by the with in-labo ratory variance, is estim ated from the residu als. In particular, the sam ple variance (3) is an unbiased estim ator of the with in-labo ratory variance. That is, the expected value of is equal to the unknown true within-la borato ry variance. Here we de® ne the with a subscript replaced by a dot to be the m ean when averag ed over the subscript that has been replaced by that dot. Thus, . Table 5 lists . If the random noises are about the sam e among the four standards for each laboratory, the best estim ate of the within-la borato ry standard deviation for each laboratory is then the pooled estim ate, and this is given in the last colum n. Sim ilarly, the last row is the pooled within-la borato ry stand ard deviation for each standard when the random noises are about the sam e among the particip ants for each stand ard. Laboratory 8 has larger with in-labo ratory variatio n than the other particip ants. Also, stand ard 3 exhibits larger noise than the other three stand ards.

Figure 4. Plot of the within-laboratory standard deviations against the m easurement time (in days).

Since the tim e spent taking the m easurem ents varied from 26 hours to 146 hours among laboratories, we plot the with in-labo ratory standard deviations again st the m easurem ent tim e in Figure 4. We also plot the within-la borato ry stand ard deviations again st the laboratory’ s tem perature range in Figure 5. Both plots reveal no apparent relatio nship betw een the magnitu de of the with in-labo ratory standard deviation and these tw o facto rs. The laboratory effect, characterized by the between-laboratory variance, is estim ated from the means of the residuals for each laboratory. Table 6 displays the mean of the residu als in

Tab le 5. Estimated w ithin-laboratory standard deviation. Estimated standard deviation/nV Lab.

S td 1

Std 2

S td 3

Std 4

P ooled

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

114 77 101 138 86 59 153 203 114 99 96 84 145 155 119 184 95

134 117 116 167 79 92 119 216 71 94 128 111 106 77 89 118 111

128 97 102 113 125 161 199 289 75 103 230 64 172 93 111 142 86

150 97 80 150 101 109 91 191 42 107 151 91 165 71 89 148 72

132 98 101 144 99 112 146 228 80 101 159 89 149 105 103 150 92

Pooled

125

118

144

118

M etrologia, 1998, 35, 33-40

Figure 5. Plot of the within-laboratory standard deviations against the temperature range (in C).

37


between-laboratory variatio ns are within the lim its of the random ¯ uctuations.

Tab le 6. Mean of LSS residuals of (2). M ean L SS residual/nV Lab.

S td 1

Std 2

S td 3

Std 4

Average

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

39 122 ±63 ±7 ±58 ±29 ±254 ±155 108 71 201 33 190 ±189 ±57 ±188 144

±168 129 105 ±23 78 91 34 ±151 ±173 ±89 6 ±43 82 ±8 87 42 ±46

365 ±31 335 57 ±115 ±103 ±378 ±378 ±147 ±120 147 38 ±46 ±171 185 85 192

90 79 ±187 ±78 30 107 30 21 47 70 46 ±147 ±316 ±112 257 51 60

81 75 47 ±13 ±16 17 ±142 ±165 ±41 ±17 100 ±30 ±23 ±120 118 ±2 87

3.3 Averaging over the four standards

Tables 5 and 6 were obtained based on the assum ption that the laboratory effects are differen t among stand ards. In this section, we estim ate the laboratory effect and the random error by averaging over the four standards. The between-laboratory and the with inlaboratory standard deviation s were found to be 80 nV and 176 nV, respectively, by the analy sis-o f-varia nce techn ique. The betw een-laborato ry standard deviation so obtained is approxim ately equal to the stand ard deviation of the residu als , that is, the residuals from the LSS ® t of (5). Again, the between-laboratory variatio n is sm aller than the with in-labo ratory variatio n, indicating that no signi® cant (average) differenc es between laboratories have been detected.

colum ns 2 to 5. It also displays the mean of the four , in the last colum n. The residuals in Table 6 can also be obtained from the LSS ® ts that are based on the averag e, rather than indiv idual, m easurem ents of the laboratories. Speci® cally , are alm ost identical to the residuals of the m odel (4) and

are approxim ately the residu als of the m odel (5)

The betw een-laborato ry variance for stand ard estim ated by

is

(6) (see [6]). The ® rst term on the righ t-hand side of (6) is the variance of the residu als or, approxim ately, the variance of the residu als from the LSS ® t of (4). The second term is a bias correction term , which makes unbiased. Thus, if the second term is sm all relative to the ® rst term , the betw een-laborato ry standard deviation is approxim ately equal to the standard deviation of the LSS residu als of (4). Values of , for , are 134 nV, 93 nV, 210 nV, and 130 nV, respectively. Now let us compare the estim ated laboratory effect with the estim ated random noise, that is, the betw eenlaboratory stand ard deviation with the with in-labo ratory standard deviation, for each stand ard. If we use the pooled estim ates 125 nV, 118 nV, 144 nV, and 118 nV in Table 5 as the within-la borato ry stand ard deviation s for the four stand ards, then each of the betw eenlaboratory stand ard deviation s, with the exception of standard 3, is not signi® cantly larger than its respective with in-labo ratory stand ard deviation, indicating that the 38

3.4 Uncertainty of the IL C

Since we com pare the between-laboratory stand ard deviation with the with in-labo ratory standard deviation to determ ine if the betw een-laborato ry variatio ns indicate any real differenc e between laboratories, an evalu atio n of the with in-labo ratory variatio ns of the comparison process used in this IL C is critical. A low er lim it to the uncertainty can be deriv ed by observing the variation of measurem ents all m ade at the sam e laboratory over a comparable period of tim e. There are tw o such data sets. one recorded at Fluke from 22 August to 4 October 1996 (128 measurem ents for four standards) and one recorded at NIST, Boulder, (739 measurem ents for four standards) from 9 October 1996 to 8 January 1997. These m easurem ent sets give data on the com bination of the m easurem ent system noise and the transfer standard noise over the tim e scale of the comparison. In the case of the NIST set, the results also include the effect of relev ant variatio ns in tem peratu re and, to a lesser exten t, relativ e humidity . Table 7 displays the stand ard deviation of the residu als to the tim e LSS ® t lin e for these tw o data sets. Note that the variatio ns of the m easurem ents m ade at NIST and Fluke are comparable with the variatio ns of the IL C data set in Table 5. This im plies that the effects of transp ort and variation s in relative humidity experienced by all stand ards are m inor compared with the m easurem ent noise and intrin sic ¯ uctuation s of the standards. The uncertain ty of the IL C is obtained by combining the betw een-laborato ry and the with inlaboratory variatio ns for the approxim ately sixty-f our measurem ents made at each laboratory. Speci® cally, the uncertain ty ( ) is nV nV. M etrologia, 1998, 35, 33-40


Tab le 7. Standard deviations of the residuals for the Fluke and N IST, Boulder, data. S tandard deviation of residuals/nV Standard 1 2 3 4

F luke 139 134 152 108

a b

NIST ±B 165 159 156 184

a. With one outlier rem oved. b. With four outliers removed.

4. Conclusions A com parison of Josephson voltage standards has been made among ® fteen stand ards laboratories in North America. The estim ated uncertain ty ( ) of the comparison is 17 parts in . Differenc es between laboratories were estim ated based on an LSS ® t using param eters of tim e and pressu re. An LMS ® t yields comparable results, indicating the absence of outlying data. Thus 100 % of the subm itted data were used in the ® t. The peak-to -peak variatio n between laboratories falls inside the estim ated uncertain ty, indicating that no signi® cant differenc es between laboratories have been detected. The calculated uncertain ty of this model is not a full measure of the reproducible level of volt traceability to NIST or the US Legal Volt for any indiv idual laboratory particip ant, and should not be directly quoted as such. The model for the four Zener stand ards does not include any system atic uncertainty and is therefo re useful only as a m eans of comparing one laboratory with another. The combined standard uncertainty for a com parison between tw o laboratories must include the com bination of each indiv idual laboratory’ s uncertain ty and the uncertainty of the m odel for each laboratory’ s measurem ent of the travelling standard. An assessm ent of each laboratory’ s uncertainty should therefore be an im portant part of future IL Cs. Alth ough comparing this IL C with previous Josephson voltage ILCs is dif® cult because differen t methods were employed to analyse the results, slightly im proved uncertainty in this ILC may be attribu ted to the inclusion of a pressure correction and the fact that the relative ly rapid pace of the measurem ents avoided long-term changes in the drift rate. Furth er im provem ent in the estim ated differen ces and their uncertainty m ay be possib le if data are obtained for at least one year in a stable laboratory before the start of the ILC. This would give a better estim ate of the inherent variatio ns of the standards and perhaps suggest a tim e interval when seasonal changes in drift rate are m inim ized. Acknowledgem ents. All participants in the ILC gratefully acknowledge the loan of the four travelling standards from the John F. Fluke Co. and the helpful advice of Raym ond Kletke on their use M etrologia, 1998, 35, 33-40

and perform ance. The Electricit y Division at NIST, Gaithersb urg, gratefully acknowledges the loan of the Josephson array chip used in their m easurem ents from Hypres, Inc. The authors thank Lawrence A. Christian , Richard L. Kautz, and Richard L. Steiner for their m any helpful comments. This work is a contribution of the Nation al Institute of Standards and Technology and is not subject to copyright in the United States. Referen ces 1. H am ilton C. A., Burroughs C. J., Kao C., O peration of N IST Josephson Array Voltage Standard, J. Res. Natl. Inst. Stand. Technol., 1990, 95, 219-235. 2. Steiner R., Stahley S., MA P Voltage Transfer Between 10-V Josephson Array Systems, Proc. 1991 NCSL Workshop and Symposium, 205-209. 3. Rodriguez K. M., Huntley L., U .S. Intercom parison of Josephson A rray Voltage Standards, IEEE Trans. Instrum. M eas., 1995, 44, 215-218. 4. H am ilton C. A ., Burroughs C. J., K upferman S. L., N aujoks G . A., Vickery A., A Com pact Transportable Josephson Voltage Standard, IEE E Trans. Instrum. M eas., 1997, 46, 237-240. 5. Rousseeuw P. J., Leroy A. M., Robust Regression and O utlier D etection, N ew York, Wiley & Sons, 1987. 6. Rao P. S. R. S., Sylvestre E. A., A NOVA and MINQUE Type of Estimators for the One-Way Random Effects M odel, Com munication in Statistics ± Theory and M ethods, 1984, 13, 1667-1673.

Received on 27 August 1997 and in revised form on 17 November 1997.

Appendix. Addition al particip ants Two additional particip ants, Centro Nacional de Metro log õ Â a (CENAM) of Mexico, and Keithley Instru ments, Cleveland , Ohio, were unable to m ake measurem ents on the original schedule. Their measurements were completed in June and July 1997, about six weeks after the end of m easurem ents by the other laboratories listed in Table 1. W hen these new data and additional NIST data were analy sed, the tim e drift rate of the standards changed relativ e to the ® rst seventeen data sets. This effect has been observed in sim ilar standards and appears to be seasonal, perhaps brought on by the increased humidity of summ er m onths. Since there were not enough measurem ents to m ake a second evalu atio n of the pressu re coef® cient, the values in Table 3 were used to correct all m easurem ents to sea level before (tim e) was estim ated. A tim e ® t to this later group of ® ve data sets (averaged over the four standards) yields the results shown in Table 8. The variatio n of the residu als is 64 nV. Withou t the pressu re 39


correction the variatio n of the residuals is 158 nV. The im provement in the variation of the residuals con® rm s the validity of the pressure correction. All ® ve measurem ents in this later set fall within the 166 nV estim ated uncertainty of the comparison, indicating again that no signi® cant differen ce among laboratories has been detected. The con® rm ation of a seasonal change in slope would suggest that the results in a voltage ILC m ay be im proved by making all m easurem ents during a perio d of tim e when the stand ards are expected to drift lin early with tim e. Alternatively, a return to the pivot laboratory procedure would allow each laboratory to compare with

40

Table 8. LSS residuals for the additional participants. Lab.

Residual/nV

Residual a /nV

18 19 20 21 22

±108 28 123 168 ±210

±50 37 19 75 ±81

a. With pressure corrected.

the drift lin e segm ent connecting the before and after pivot laboratory results.

M etrologia, 1998, 35, 33-40