*From t√√n where a is estimated to be 0.00017g based on the pooled standard deviation of silicon weighings (9 degrees of freedom). The Student-t statistic for a 99% confidence interval in this case is 3.25. The residual standard deviation from this fit is 9.6 x 10-7. The target absolute residual of the polynomial values from those of Gibbons is 2.5 x 10-6 which occurs for T = 240 K. This maybe an aberrant point, the next largest in absolute value is -1.7 x 10-6 for T = 90 K. A plot of these residuals show a non-random pattern, so another method of interpolation may improve the fit. The estimated standard deviations for the values of B(T) predicted by the above polynomial range from 7.8 x 10-7 at 70 K and 300 K to 3.4 x 10-7 at 150 K. If determination is approximately lap/al=c(2.3 × 10−6), 10-5 Thus, if g/cm3 (.007%) 3 eq (4) is used fo the B(T) calculation, another 1.6 x would be added in quadrature to the total in table 2. Even if this error were a factor of 10 larger, it would contribute little to the total systematic error. 4. CALCULATIONS OF THE RANDOM UNCERTAINTY FOR THE PORTABLE DENSIMETER The PRD has been tested in the Density Reference System. The accuracy and precision of the DRS densimeter and the portable densimeter are essentially independent of liquid composition. Their accuracy and precision depend primarily upon the accuracy and precision of the balance and how well the weight and density of the silicon crystals are known. The ability to make an accurate comparison will, of course, depend upon conditions within the sample holder. The liquid needs to be relatively quiet, well mixed and of a fairly uniform temperature in the volume in which the measurements are being made. The liquids chosen for comparing the two densimeters were saturated liquid methane and a saturated LNG like mixture. The DRS densimeter has been tested in those liquids [3]. The comparison of the two densimeters is based on data taken from two fillings of the liquid sample holder, for a total of 35 density values. We first filled the DRS sample holder with liquid methane, took a series of measurements in the range of 110 to 125 K, then added nitrogen (about 1% to 2%) and propane (about 4% to 6%) to simulate LNG and took another series of measurements in the same temperature range. The series of measurements for a liquid sample in the DRS were made by either heating or cooling the saturated liquid to a target temperature, waiting for the liquid to come to equilibrium, and taking the desired schedule of readings. The sample was stirred and the readings were repeated giving a duplicate set of readings for each temperature. It is reasonable to assume that the random error of the duplicate density values described above would correlate more closely than values obtained at another temperature. Because of the large correlation between duplicate readings, only one of each of the duplicates can be usefully employed in the analysis. We have arbitrarily chosen to use the first of each duplicate in our analysis. The second of each would provide essentially the same information. Using both duplicates would complicate the analyses without providing any increase in information. e where PTij is the jth density determined by the portable densimeter on the ith set of runs, PDij is the corresponding density value determined by the DRS densimeter, μ represents any systematic difference between the two methods, aj represents a shift in the mean for measurements on the ith set of runs, and eij represents any random contribution to the jth measurement on the ith set of runs. A set of runs are those measurements made with a particular mixture in the liquid sample holder. Apij' There are four Figure 2 is a plot in chronological order of the sets of runs shown in this figure, two for methane and two for the LNG like mixture. The symbol "M" is for a methane value and "L" is for LNG. In this plot can be seen the extent of any shifts, a¡, in the mean of the AP¡j from one set of runs to the next. We know from our study of the DRS, ref. 3, that such shifts occur and appear to be random. In the DRS study, only methane data was used to study the variability of the a, because the comparison was between the DSR densimeter and the Haynes-Hiza [5] temperature relationship for saturated liquid methane. Because the Haynes-Hiza relationship depends on pure methane, the a.may have partly been the function of contaminants in the methane. The 99% upper bound on the standard deviation of the Apij, taken from ref. 3, is .036 kg/m3. This is the bound we take to represent the variability from one set of runs to the next for each of the two Archimedes densimeters that we are |