have a negligible systematic effect on the temperature. Lag corrections were not applied to the temperature data because of the small size of such a correction and its large relative uncertainty under actual experimental conditions.

On a time scale which is short compared to the response time of the thermometer, the temperature in the balance case is complex. This was learned by observing the thermocouples. Upon introducing one of the large-volume weights into the balance, the temperature as measured by the 13 thermocouples fell in a matter of seconds by as much as 200 mK. After about one minute the temperature of the thermocouples was seen to have risen to a slightly warmer temperature than observed before the weight was introduced. That this behavior is not observed with the artifacts of smaller volume may be a consequence of the distance of their surfaces from the thermocouples. Because the test weights are not isothermal with the balance enclosure during the measurements, the choice of the proper temperature to apply in computing the density of air is ambiguous. Although we assume an uncertainty in temperature of 30 mK, this number must itself be viewed as uncertain.

at NBS and Sandia. These results are summarized in tab 4. Since the measurement of CO2 concentration in ar given sample can be made with an uncertainty of 25 ppm the concentration, the observed standard deviations at NE I and Sandia represent real fluctuations of the CO2 concer tration in the balance case. As these fluctions may be observed between daily readings, we feel that the standar deviation of the fluctuations is a reasonable estimate of o uncertainty in the CO2 concentration in the balance cas The average obtained for NBS III agrees excellently w previous measurements of ambient air at NBS. We canr explain the significant difference between the NBS I aver age and the other NBS data.

4.1.2. Pressure

The aneroid barometers used were calibrated twice daily against instruments which can read pressure with a relative uncertainty of 5 × 10-5 (mercury manometer and quartz transducer; see above). The aneroids themselves are known to deviate by as much a 0.1 mm of Hg (1 mm of Hg equals 133.3224Pa) from their calibrated value over the course of a day. Therefore the uncertainty in the pressure inside the balance case was less than 0.1 mm of Hg, a number which, we feel, approximates one standard deviation.

4.1.3. Relative Humidity

A well-behaved and well-cared-for Dunmore-type hygrometer will retain its calibration to better than 0.5 percent relative humidity for long periods of time [11]. Our elements were checked against salt solutions [8, 12] the vapor pressure of which was in the middle of the range of the humidity element. These checks established the stability of the Dunmore-type elements to 1 percent relative humidity. Temporal changes observed in the humidity sensor readings over standard salt solutions were used to estimate uncertainties in the readings. These deviations were not viewed as changes in the calibration of the elements.

4.1.4. CO2

The carbon dioxide content of the air in the balance case was measured twice daily during the 48 four-ones series run

The CO2 concentration was not measured during the fina weighings at NBS which were performed in a temperature controlled room. Instead, a value of 430 ppm by volume was assumed. We estimate an uncertainty of 100 ppm in the concentration as a result of this assumption. This uncertai ty propagates as an uncertainty in o of 40 ppm [2] and a uncertainty of less than 15 μg in the assignment of mass to an aluminum kilogram as calibrated against a stainless ste standard.

4.1.5. Volume of the Artifacts

The volume of each artifact was determined by hydr static weighing with independent mechanical checks for those with simple geometry. It is believed that all volumes are known to about 50 ppm. Of course, the volumes vary with temperature but this effect is small (<70 ppm/°C in a cases) and, therefore, easily estimated to sufficient accu racy. Note that even a 1 percent error in o could be toler ated in a hydrostatic determintion of volume to 50 ppm.

4.1.6. Air Density Equation

The use of an equation to determine the density of air entails errors apart from the instrumental inaccuracies outlined above. In a meticulous examination of the equation used in this study [2], Jones cites relative uncertainties of 50 ppm random and 50 ppm systematic independent of inaccu racies in the measurements of input parameters. These numbers treat the uncertainty in R, the ideal gas constant,

as a random error. In using the air density equation, however, the uncertainty in R becomes a systematic error in Q. Thus the relative uncertainties in the calculation of g become 40 ppm random and 80 ppm systematic. These represent one standard deviation.

4.2. Uncertainty in the Buoyancy Correction

We may now calculate the uncertainty expected in applying buoyancy corrections to our weighings. There are two uncertainties of interest: random, which introduces scatter in the measurements, and systematic, which introduces errors in the average values obtained. In particular, we are concerned with an estimate of the maximum expected difference between mass measurements of the same artifact at NBS and at Sandia due to known systematic uncertainties in the buoyancy correction.

Table 5 summarizes the random uncertainties expected in the calculation of the density of air, o. These will lead to random uncertainties in the buoyancy corrections of 50 μg for A, H1, and H2; 15 μg for T; and virtually zero for R1, R2, S1 and S2. These numbers assume usual laboratory conditions at NBS. At Sandia, the random uncertainties are calculated to be 20 percent smaller bacause the buoyancy correction is itself 20 percent smaller than at NBS.

The relatively smaller magnitude of the buoyancy correction at Sandia compared with that at NBS leads to the possibility of systematic differences between masses measured at the two locations. These descrepancies arise from systematic errors in the calculation of Q as well as from errors in AV, the assignment of volume difference between an unknown weight and the standard. Table 6 details the known sources of systematic uncertainty in Q, while table 7 indicates the resulting uncertainties in comparing the mass of an artifact as measured at NBS with the mass of the same artifact as measured at Sandia.

Although not indicated in table 7, the sign of systematic errors due to o is opposite for weights which are more dense and less dense than the standards.

Thus the maximum systematic difference to be expected, at a level of one standard deviation, i. e. in measurements of H1, H2 and A, is smaller than the standard deviation of the balances used in the measurement. It should be emphasized that the only systematic effects considered in table 7 are those associated with applying buoyancy corrections to the data obtained from readings of the balance.

In order to evaluate the results, we must establish a criterion by which to assess the significance of any discrepancies observed among sets of data. Referring to figure 1, one sees that the average standard deviations of all four NBS data sets are roughly the same and equal to about 40 μg. The average standard deviation at Sandia was 60 μg. Using these numbers to define the experimental standard deviations at NBS and Sandia, we can calculate by well known techniques [14] whether the means of different sets of data differ at the 0.05 level of significance. These calculations depend on the number of independent measurements in the data sets being compared. Table 8 is a compendium of the various statistical conditions pertaining when one compares results which are plotted in figures 3-10.

At the level of significance chosen, there definitely remain systematic differences in the masses of the same object computed at different locations or times. Note that some of these systematic differences occur in objects whose volume is nominally the same as that of the standards, a situation which is nearly insensitive to systematic errors in buoyancy correction.

Certain trends may be inferred from the systematic differences among the data sets. In general, the extremal values of the various mass determinations were found at NBS I and Sandia. Computed mass values obtained at NBS III and NBS IV agree well with Sandia values while NBS II values fall between those of NBS I and the others. These features are unchanged if the data are reanalyzed using direct comparison with the standards instead of a least squares solution to a four-ones series.

Specifically, let us compare the Sandia results with those of the other series. These comparisons are displayed in table 9. It is striking that 70 percent of the numbers displayed are negative. The tantalum weight as well as R2 and possibly H2 are the only weights immune to the negative systematic difference. Many of the differences, when looked at alone, are within reasonable expectations as calculated in the preceding paragraphs. When taken as an ensemble, however, the systematic behavior is apparent.

-68

Differences between weights measured at Sandia (S) and at NBS. Thes differences, measured in milligrams, are tabulated as a function of difference between the volume of the weights in question and the sta dards B1 and D2.

The behavior of S1 and S2 (figs. 7 and 8) suggests tha surface effects, related to temperature, may play a role the measurements. In fact, when the difference in mass S1 and S2 is plotted as in figure 13, there remain no signi cant discrepancies as a function of place or time. Simil graphs of H1,R1 and H2,R2 (figs. 11 and 12) indicate significant difference between the measurements of NBS and the remainder of the data. We have no way to elimina surface-related effects in the measurements of A and T.

The appearance of surface effects is not likely to be du to moisture. A simple calculation indicates that about s monolayers of water would have to be removed from th standards and S1 and S2 to account for the systematic d.. ferences observed between measurements at NBS and Sar dia. The data of Kochsiek on the moisture content of stair less steel surfaces [13] render this possibility untenable.

It seems to us likely that the cause of most of the sy tematic scatter in the data is the absence of thermal equ librium between the artifact weights and the balance. Thabsence of equilibrium may manifest itself as a force whi depends qualitatively on the shape or surface area of the weights. Such effects have been observed in small weigh[15]. In addition, the buoyancy correction assumes equi rium conditions. The measurements designated NBS II were an attempt to duplicate the thermal environment Sandia as nearly as possible. To this end measuremer were conducted at 21 °C in a temperature controlled room Table 4 suggests that the duplication of the Sandia therma conditions did come closer than the other NBS measur ments to duplicating the Sandia data. Nevertheless, none the measurements were done at thermal equilibrium conc tions if one considers 0.2 °C fluctuations as significan

early it is desirable to perform the above measurements ider isothermal conditions. A thermostated balance enclore and a weight-changer which will accommodate lownsity kilograms were already under development before e measurements reported above were undertaken. These odifications, when completed, will permit controlled study the effects reported above.

It should be emphasized that the largest systematic difrences observed are more than a factor of five smaller an those which occasioned the publication of [1].

An additional, unexpected result deserves mention. Our ata show that unpolished aluminum bar stock is wellehaved as a weight. That is, the least-squares mass soluons to four-ones weighing series which contained A as one f the weights showed consistently lower standard devia-ons than four-ones solutions of all-stainless steel weights. It has been suggested that a pair of weights having nomially equal masses and surface areas but very different olumes be used to determine air density in a balance [3]. The combinations H1,R1 and H2,R2 are such pairs. In paricular, we have measured the difference in mass of H2 and 12 thirteen times at NBS and three times at Sandia. The tandard deviation of the NBS differences is 87 μg. These neasurements were taken over a period of five months. The observed standard deviation may be taken as an indication of how well the two-artifact method of inferring the buoyany of air agrees with the method actually used in our measurements. The disagreement indicates a random uncertainty (1 standard deviation) in the application of the two-artifact method of ~300 ppm-this is consistent with the results of other experiments [3,16]. This uncertainty is also, to an unknown extent, subject to the systematic effects which we have discussed at length above. In spite of this, however, two observations may be made: 1) The data taken at Sandia do not differ significantly from the NBS results and 2) the 300 ppm uncertainty in the measurement of o by the two-artifact method is consistent with the minimum random uncertainty expected for use of the air density equation with state-of-the-art measurement of input parameters [2].

5. Conclusion

1. Five groups of measurements of the mass of an aluminum and a tantalum kilogram against stainless steel standards were carried out over a period of several months. Four groups of measurements were made at NBS, Gaithersburg and one at Sandia Laboratories in Albuquerque. While the groups of data exhibit significant differences amongst them of the type reported in [1], the magnitude of these discrepancies is a factor of five less than had previously been observed by the author of [1]. We remain unable to reproduce or satisfactorily explain the earlier results.

2. The results using weights with purposely enhanced surface area and weights of stainless steel with artificially low density indicate that surface effects likely play a role in our observed discrepancies.

3. The systematic discrepancies which are present in our results cannot be explained by buoyancy effects since these discrepancies exist between objects which have nearly identical volume. Our hypothesis is that the observed behavior is due to the weights not being in sufficiently good thermal equilibrium with the balance. This hypothesis will be explored using apparatus now under construction.

4. In the present experiment, the procedures followed to tie measurements of pressure, temperature, and relative humidity to absolute standards were the most rigorous which are likely to be used for routine mass calibrations of high precision. In addition, extraordinary precautions (short of remote control) were taken to reduce the effect of operator proximity on the measurements. We believe our results demonstrate the systematic errors which may be expected even under these circumstances.

A number of people have been extremely helpful during the course of these measurements: Charles Reeves of the NBS Statistical Engineering Division aided in the design and analysis of the experiment. The staff of the Primary Standards Laboratory of Sandia Laboratories generously lent their facilities and technical support. In particular, the cooperation of Merrill C. Jones, Arnold B. Draper, David W. Braudaway, Robert B. Foster, Frank E. Anderson, Sandra L. Anderson and William Schuessler is gratefully acknowledged.

6. References

[1] Pontius, P. E., Science 190, 379 (1975)

[2] Jones, F. E., J. Res. Nat. Bur. Stand. (U.S.) 83, 419 (1978)

[3] Koch, W. F., Davis, R. S., Bower, V. E., J. Res. Nat. Bur. Stand. (U.S.) 83, 407 (1978)

[4] Powell, R. L., Hall, W. J., Hyink, C. H., Jr., Sparks, L. L., Burns, G. W., Scroger, M. G., Plumb, H. H., NBS Monograph 125—Thermocouple Reference Tables Based on the IPTS-68 (Nat. Bur. Stand. (U.S.), March 1974) pp. 90-102

[5] Riddle, J. L., Furukawa, G. T., Plumb, H. H., NBS Monograph 126— Platinum Resistance Thermometry (Nat. Bur. Stand. (U.S.), April 1973)

[6] Harper, D. R., III, Bul Bur. Stand. 8, 659 (1912)

[7] Brombacher, W. G., Johnson, D. P., Cross, J. L., NBS Monograph 8— Mercury Barometers and Manometers (Nat. Bur. Stand. (U.S.), August 1964)

[8] Stokes, R. H., Robinson, R. A., Ind. and Eng. Chem., Analyt. Ed. 41, 2013 (1949)

[9] Cameron, J. M., Croarkin, M. C., Raybold, R. C., NBS Tech. Note 952-Designs for the Calibration of Standards of Mass (Nat. Bur. Stand. (U.S.), June 1977)

[10] Pontius, P. E., Cameron, J. M., NBS Special Publication 300-Precision Measurement and Calibration, Ku, H. H., Ed., Vol. I-Statistical Concepts and Procedures (Nat. Bur. Stand. (U.S.), Feb. 1969) pp. 1-20

[11] Handegord, G. O., Hedlin, C. P., Trofimenkoff, F. N., Humidity and Moisture Measurement and Control in Science and Industry, Wesler, A., Ed.-in-chief, Vol. I—Principles and Methods of Measuring Humidity in Gases, Ruskin, R. E., Ed. (Reinhold Publishing Corp., N.Y. 1965) pp. 265-272

[12] Meites, L., Handbook of Analytical Chemistry (McGraw-Hill Bo Co., Inc., N.Y. 1963) p. 3-29

[13] Kochsiek, M., PTB-Mitteilungen 87, 478 (1975)

[14] Natrella, M. G., NBS Handbook 91-Experimental Statistics (Ng Bur. Stand. (U.S.), Aug. 1963), Chapter 3.

[15] Blade, E., Ind. and Eng. Chem., Analyt. Ed. 12, 330 (1943) [16] Toropin, S. E., Snegov, V. C., Izmeritelnaya Tekhnika 12, 75 (1975) English trans.: Meas. Tech. 19, 1847 (1976)