pleted in approximately four hours. In each case, the data were corrected for decay to the same time. The consistency of the source measurements using the two chambers was tested by summing the currents and determining the frac tion of the total current contributed by each seed. The standard deviation of the ratios of the seed calibrations for these two sets of measurements is 0.2 percent with one outlier of 1.2 percent included.

The calibration factors for the re-entrant chambers are the quotients of the exposure rate, for the seed array in the open-air measurement, and the sum of the individual currents produced by the seeds in the re-entrant chambers. The factors for the plastic and aluminum spheres determined for the platinum-encapsulated seeds, as well as the factor for

the stainless-steel-encapsulated seeds in the aluminum chamber, are given in table 7. The calibration factor determined for the stainless-steel-encapsulated sources in the aluminum chamber is 3 percent different from that deter mined for the platinum-encapsulated sources.

Because of the relatively short half-life of iridium-192, the reference for exposure calibrations for this isotope will be the re-entrant chamber and its calibration factors. Although the chamber design is such that no problem with constancy is foreseen, a 0.5 mg radium source, in a special plastic thistle tube for handling, has been used as an overall reference source throughout the measurements. This source will be used to insure the consistency of all iridium source measurements in the future.

rs

The statistical uncertainty for the long-term reproducibility of the measurements deserves special comment. To arrive at the value given in table 8, the data from table 6 were corrected using the values for k,, and kas and then corrected to a common distance via the inverse square law. The standard deviation of those five ab initio measurements is 0.5 percent and the standard deviation of the mean is 0.2 percent. The value given in table 8 is three times the standard deviation of the mean of the five measurements. Although statistical effects of current and distance measurements influence these data, they do not significantly affect the outcome. While the differences between the means of the corrected data for 0.5 m and 1.0 m measurements indicate a possible inadequacy in the corrections for attenuation and scattering, there are not enough measurements to support this conclusion and this difference can be either statistical or systematic.

The quadratic sum of the systematic uncertainties is 0.7 percent, and like treatment of the statistical uncertainties gives 0.6 percent. If all of these uncertainties are added in quadrature an estimate of the overall uncertainty is 1 per

TABLE 8. Estimated uncertainties in the determination of the exposure rate at one meter from an iridium-192 seed.

Uncertainty (%) Systematic Statistical

Standard chamber: Air volume

Corrections:

Wall Absorption Stopping power Energy absorption Recombination Stem scatter

Scattering:

Room surfaces

Air attenuation and scatter

Current at one meter (open-air):
Current
Humidity
Temperature
Pressure

0.02

Reproducibility (long-term)

0.6

Distance

cent. But since this is a new calibration service, and in the absence of checks from other laboratories, we propose to take the overall uncertainty associated with an iridium seed calibration as 2 percent.

calibration factor for 10-mm-long iridium-192 wires are given in table 9.

TABLE 9. Iridium-192 wire-length correction factors relative to the aluminum re-entrant chamber calibration factor for a 10-mm-long wire.

Length (mm)

9. Addendum

After the work described in this article was complete the Radiological Physics Center at M.D. Anderson Hospital in Houston requested exposure calibrations of platinumencapsulated iridium-192 wires which were 10 mm, and 50 mm, long. All other dimensions of the wires were the same as described in table 1. Since the calibration factors for the re-entrant chamber had been determined for seeds which lay almost horizontally in the re-entrant tube and the longer wires would stand almost vertically, it was necessary to determine a new re-entrant chamber calibration factor for this condition.

Nine 10-mm-long wires and two 50-mm-long wires of high specific activity were provided by the Radiological Physics Center. The 10-mm wires were immobilized in the plastic holder used for the stainless-steel seed measurements, and open-air measurements using one of the standard graphite ionization chambers were carried out as already described. The exposure rate from this group of sources on the reference date was determined to be 2.051 nA kg ̄1·m2 (7.951 R sm2).

-1

The wires were removed from the plastic holder and each wire was measured individually in the re-entrant chamber. The sum of the currents, corrected for recombination and corrected to the reference date, was 2416 pA. The quotient of the open-air group exposure rate, and the total re-entrant chamber current, is the aluminum re-entrant chamber calioration factor for 10-mm-long platinum seeds. The calibraion factor is 0.8489 m2 kg' and, in special units, is 3.290 R s1 m2 A'. Thus, the re-entrant chamber response for he 1-cm-long wires in the upright position is 1 percent greater per unit exposure than the response for the 3-mmong seeds.

The dependence of the re-entrant chamber response on he length of the iridium-192 wire was found by measuring he current produced by one of the 10-mm-long sources as it was raised in 10-mm increments up the re-entrant tube. A hread affixed to the end of the wire was used for this purpose. Correction factors relative to the re-entrant chamber

Correction factor

[1] A Manual of Radioactivity Measurements and Procedures, Nat. Council on Radiation Protection and Measurements Report No. 58. P.O. Box 30175, Washington, DC 20014.

[2] Martin, M., Nuclear Data Project, ORNL. Oak Ridge, Tennessee 37830. (Priv. Comm. May 1977)

[3] Hubbell, J. H., Photon Mass Attenuation and Mass Energy-Absorption Coefficients for H, C, N, O, Ar, and Seven Mixtures from 0.1 keV to 20 MeV. Radiat. Res. 70 58-81 (1977).

[4] Loftus, T. P. and Weaver, J. T., Standardization of "Co and 137Cs Gamma-Ray Beams in Terms of Exposure. J. Res. Nat. Bur. Stand. (U.S.A.) Physics and Chemistry, 78A, No. 4 (July-August 1974).

[5] Nelms, A. T., Graphs of the Compton Energy-Angle Relationship and the Klein-Nishima Formula from 10 keV to 500 MeV, National Bureau of Standards (U.S.) Circular 542, 89 pages, Aug. 28, 1953.

[6] Berger, M. J. and Seltzer, S. M., Tables of Energy Losses and Ranges of Electrons and Positrons, NASA SP-3012, 1964 (available from the Clearinghouse for Scientific and Technical Information, Springfield, Virginia).

[7] Eisenhauer, C., An Image Source Technique for Calculating Reflection of Gamma Rays or Neutrons, Health Physics 11, 1145-1154 (1965).

[8] Eisenhauer, C., A study of the Angular and Energy Distributions of Radiation at Small Distances from a Point Source of Gamma Rays or Neutrons, Nuclear Science and Engineering, 27, 240-251 (1967).

1. Introduction

In 1975 results were published of a series of measurements undertaken by the National Bureau of Standards (NBS) of the mass of aluminum and tantalum artifacts as determined by comparison against standards of stainless steel [1].' The paper reported inconsistencies which seemed to be correlated with barometric pressure. The stated magnitude of the unexpected effect is 1 mg in 1 kg over a pressure range from 0.5 to 2 atmospheres for objects having a volume difference of 200 cm3. The sign of the effect was not reported in [1]. The inconsistencies or "anomalies" as they were termed were observed between laboratories near sea level and those at an altitude of ~ 1600 m. Quantitative results of these measurements are not given in the An paper. examination of the original data, however, shows that an aluminum kilogram (density ~ 2.8 g cm3) was measured to be 830 μg lighter compared to a stainless steel standard (density 7.8 g cm3) at the higher altitude than at sea level. The tantalum kilogram (density 16.6 g cm3), on the other hand, was found to be 275 μg heavier than at sea level. A conclusion of [1] is that buoyant forces on objects placed in air are incorrectly accounted for by the usual means of computing Q, the density of air, from an equation whose input parameters include barometric pressure, temperature, relative humidity, and sometimes, CO2 fraction. Recently, Jones [2] has published a careful reformulation of the air density equation. He concludes that, using stateof-the-art measurements of pressure, temperature and rela

'Figures in brackets indicate literature references at the end of this paper.

tive humidity, the following relative uncertainties are to be expected in o: 300 ppm (parts per million) random, 200 ppm systematic at a level corresponding to one standard deviation.

Koch, Davis and Bower [3] have intercompared two objects of different density to determine their mass difference both in vacuo and in air. From these measurements, they can test Jones' air density equation. The agreement is well within their experimental uncertainty of 600 ppm in Q.

In an effort to reconcile these measurements, which are consistent with Jones' air density equation, with those summarized in [1], the following experiment was undertaken. A series of weighings at NBS, Gaithersburg, was made with a selection of kilogram artifacts. Similar measurements with the same artifacts were also carried out at Sandia Laboratories, Albuquerque. The NBS, Gaithersburg, laboratories are near sea level while Sandia is 1600 m above sea level. The artifacts chosen included the aluminum and tantalum kilograms used in [1] as well as several other weights designed to elucidate surface effects. A great deal of care was taken to tie measurements of pressure, temperature and relative humidity directly to primary standards.

A very brief review of the principles involved in these measurements may be useful. Consider the comparison of two kilograms of nominally equal mass. Let M and V be the mass and volume of the standard, let M, and V, be the mass and volume of the unknown, and let o be the density of air inside the balance case. The balance responds to forces. Under equilibrium conditions, there are two forces which must be considered: gravitational, and buoyant. Thus an intercomparison of the weights will yield the result:

Measurements at both Sandia and NBS were carried out on commercially available kilogram balances. The balances were single-pan of conventional design and each had a precision of 25-50 μg.' Two modifications to the balance case were made. The original glass door on the left side of the balance was replaced with one having a port which could accommodate a Dunmore-type humidity element. In addition, an annex to the balance was constructed and placed in contact with the glass door on the right side of the balance. The annex was made of metal but had glass doors and a glass floor. The floor-height of the annex was made equal to that of the balance. The annex was made large enough to accommodate the four one-kilogram weights used in any given intercomparison. Since the balance case had no room for weights in addition to whatever was on the pan, it was hoped that the annex would help minimize changes in ambient conditions as the weights were manipulated in the course of a measurement.

Manipulations were performed by an experimenter seated in front of the balance. The experimenter wore an apron of metallized Mylar to reduce the effect of his presence on the temperature of the balance. In addition, the experimenter's right hand (used for weight manipulations) was covered by an inner cotton glove and an outer surgical glove. The purpose of the gloves was to help insulate the balance and annex from changes in temperature and hu

The precision of the balance is determined from the experimental scatter (1 S.D.) in a set of repeated measurements of a single weight the density of which is close to that of the built-in balance weights and counterpoise. Thus the measurement of the precision of the balance is unaffected by the usual fluctuations in the density of air in the balance case.

2.2. Weights

Ten different one-kilogram weights were used in the experiment. Their designations and major features are shown in table 1. The most conventional weights, B1 and D2, were used as standards. They have the desirable properties of

Artifact Designation

B1

TABLE 1

Nominal Mass (Kg)

Volume (cm3) at 20 °C

Nominal Surface

Area (cm2)

1

127.385

145

D2

1

127.625

145

HI

1

337.381

270

single-piece stainless steel construction, knobs for ease of handling, and nearly minimum surface area. Weights HI and H2, also of stainless steel, were designed to have a den sity near that of aluminum. They are hollow, right circular cylinders of minimum surface area (diameter equal to height), each having an internal center-post to lend rigidity to the end-pieces. The hollow weights are filled with helium at roughly one atmosphere pressure. The two weights R1 and R2 were constructed as companions to the hollow weights. They are solid thick-walled stainless steel tubes whose surface areas are nominally equal to those of H1 and H2. Two additional weights, S1 and S2, of solid stainless steel but with surface areas roughly twice those of the R weights were also included. The S weights are each in the form of two nested stainless steel tubes reposing on a circular, stainless steel base. A centerpost welded to the base allows easy manipulation of the S weights. The final two ar tifacts in the assemblage were single-piece weights of aluminum and tantalum, designated A and T. The alumi num weight, constructed of bar stock, is in the form of a right circular cylinder of minimum surface area. The tantalum weight is of single-piece construction of nearly minimum surface area with a knob for ease of handling. The aluminum and tantalum weights are the same ones as were used in the experiments reported in [1]. The weights were lifted with hand-held instruments designed for the pur

pose.