by any reasonable assumption of either errors in the measurements or secular changes in gravity.

During these measurements the vacuum chamber was over-constrained in its attachment to the carriage, the flat parallel ends of the chamber rested between the two parallel cross members of the carriage with a light friction fit and were secured against lateral movement by centering screws. The latch from which the carriage was suspended was attached directly to the upper cross-member of the carriage just above the vacuum chamber. It was suspected that the chamber was being loaded eccentrically by distortions of the carriage frame resulting from release of the latch. If such eccentric loading should cause some elastic bending of the vacuum chamber during the fall with a resultant rotation of the optical windows, the effect could be significant.

The displacement of the image of an object viewed through a plane-parallel glass plate is sensitive to tilt of the plate. The displacement for small angles of tilt is on the order of

where T is the plate thickness,

is the angle of tilt and N is the index of refraction. For a thickness of 4.5 mm and an index of refraction of 1.5 a rotation of one minute of arc will produce an apparent displacement of about 0.4 μm.

On the hypothesis that sufficient flexure of the chamber was taking place to produce window rotations of this order of magnitude, and that the amount of flexure would vary with slight differences of temperature between the brass chamber and aluminum alloy carriage, the vacuum chamber mount was redesigned. The chamber was slightly shortened to produce a positive clearance at the upper end in the carriage and a single point support was provided at the lower end on the central axis of the chamber.

The modification effectively eliminated the longterm variations in the observations. Later, when the apparatus was moved from the older site in the East Building of the Bureau to the new Gaithersburg site where the observations reported here were made, the carriage itself was modified. The connection between the latch and the carriage was made through two independent yokes which were attached to the carriage at points directly above the two vertical tubular structures. This arrangement eliminated the flexing of the cross-members supporting the vacuum chamber.

7.8. Time Constants of the Circuits

The 10-stage photomultiplier tube used in the measurements had a spectral sensitivity peak in the 400 to 500-nm range and was always used in the dark-to-light transition condition. Connection to the coupling amplifier circuit was less than 5 cm long and unshielded to minimize capacitance loading of the anode. The anode current was limited to 0.1 mA at full illumination. The entire phototube circuit through the coaxial cable connections to the timer panel was

capable of following illumination rise times at least five times greater than those provided by the gravity apparatus.

7.9. Uncertainty in the Length Standard

Of the two standards employed in the measurements, length and frequency, the length standard was by far the more critical in terms of the difficulty in obtaining the desired precision in its calibrations. The standard, an H-section scale of invar was ruled by the Société Genovoise. The 1-m length was graduated into 1-mm intervals. The width of the engraved lines was approximately 5 μm. Only the 0-, the 300-, and the 1000-mm lines were used in the measurements. The calibrations of the scale were limited to the intervals defined by those lines.

Table 1 shows the results of the calibrations of the scale made by the Length Section of the National Bureau of Standards. No determination was made of the 300-mm interval in the 1961 calibration because of the very small change observed in the 1000-mm interval. The table shows that the standard deviations over the five-year period compare very favorably with the estimated limits of error for the individual determinations. Since the scale was in active use over the greater part of the five-year period, it was concluded that the stability was excellent with no significant drift. The mean corrections were selected as giving the most reliable values for the lengths of the two intervals.

Some estimate of the effect of the different length determinations obtained for the invar scale can be made by computing a series of gravity values in which the successive length corrections are the only variable. Using the adopted mean corrections as a reference, the calibrations of 1960, 1962, 1964, and 1965 would have resulted in gravity values differing from the reference level by +0.5, +0.7, -1.0, and -0.2 mGal respectively. The standard deviation of the mean correction would be 0.4 mGal. This result illustrates one disadvantage in the use of an intermediary standard in a measurement requiring the greatest possible accuracy.

7.10. Uncertainty in the Length Measurements

As previously indicated in Section 4.1, a determination of the two lengths, L, and L2, of a silica tube consisted of ten measurements of each length with the invar scale on one side of the carriage and ten measurements of each length with the scale on the other side. The two sets were averaged to give the final value. The individual sets showed good internal consistency even though a set required about one hour to complete. The standard deviation of a single length determination of either the 300-mm or the 1000-mm interval was usually on the order of 0.6 or 0.7 μm; thus the standard deviation of the mean of ten would be on the order of 0.2 μm. As indicated earlier, there was usually some evidence of real change in the interval lengths over the complete series of free-fall experiments.

An interesting side effect in the length measurement is the small error due to the relative shortening of the

invar scale and the silica tube when they are supported at rest in vertical positions. The length desired is, of course, that of the silica tube in its relaxed condition in free fall. The length of the invar scale is determined in the length laboratory in a horizontal position while supported at the Bessel (Airy) points. Neglecting the slight droop of the bar between the support points, it can be considered in a relaxed condition during this comparison. If now the scale and the tube are supported on their lower ends in a vertical position, both will be compressed slightly under their own weight. The changes in lengths are in proportion to the ratio of the densities of the materials to their respective moduli of elasticity.

The decrease in length of a rod or tube standing on its lower end is given by the relationship

Although these corrections are below the level of significance in the measurements, the differences were systematic and were applied in the adjustment of the lengths of the fused silica tubes.

Since the temperature of the silica tube was not measured directly, the assumption was made that it tended to remain at some relatively stable level in relation to the temperature of the vacuum chamber which surrounded it. Some indication of the validity of this assumption can be obtained from an auxiliary set of measurements made on a brass tube of identical size and construction as the fused silica tubes from which the formal determination was made.

The brass tube was subjected to an identical set of alternating length measurements and free-fall measure

ments as were the fused-silica tubes. The set of experi ments with the brass tube followed immediately upon the conclusion of the determinations with the four silica tubes. The decision was made at the outset that regardless of what result was obtained with the brass tube, the result would not be included in the value of gravity to be reported.

The length intervals for the brass tube were measured at vacuum chamber temperatures ranging from 21.88 to 22.00 °C and corrected to 22 °C using a coefficient of thermal expansion of 18.5 × 10-6 per degree Celsius. The results are given in table 5.

Brass has a temperature coefficient such that a change of 0.1 °C would change the 1-m length by nearly 2μm. The table indicates that, aside from a single shift between the first two measurements of the 1-m interval, the brass tube showed as good repeatability as the fused silica tubes. Since the temperature coefficient of thermal expansion of brass is about 27 times that of fused silica, the evidence appears to substantiate the assumption that the temperature of the falling object followed that of the vacuum chamber reasonably well.

7.11. Uncertainty in the Final Result

From the foregoing discussion of systematic error it is concluded that the principal known source of error of a systematic nature lies in the uncertainty in the value of the length standard. The uncertainty in the time standard is too small to affect the final result significantly.

Effects such as seismic disturbances, lunar and solar tides and random errors in the time and length measurements are included in the variability of the gravity values shown in tables 3 and 4. The uncertainty in the final result is considered to be due principally to the contributions of this variability and the uncertainty in the evaluation of the invar length standard.

From the standard deviations of 0.00021 cm/s2 for the length and time measurements and of 0.00039 cm/s2 for the length standard, it is estimated that the uncer tainly in the final result is represented by a standard deviation of 0.00045 cm/s2.

8. Comparison with Other Gravity Values

The mean value of 980.1011 cm/s2 given in table 4 is that determined directly from the measured parameters of the experiment. Since there is a gravity

urement site is designated NBS-1 and the reference site is designated NBS-2.

The elevation of NBS-2 was established by a first order survey by the Levelling Branch of the Coast and Geodetic Survey, Environmental Science Services Administration, U.S. Department of Commerce.

Gravity meter connections linking NBS-1 and NBS2 to the national gravity base in the Department of Commerce Building were made in November 1965 by the Gravity and Astronomy branch of the Coast and Geodetic Survey. These connections also included the station in the sub-subbasement of the East Building where Heyl's absolute measurement had been

made.

A summary of the gravity differences taken from the report of the Coast and Geodetic Survey is given in table 6. The differences are referred to the national gravity base, specifically the top of the east elevated pier in the gravity room of the Commerce Building. The gravity meter observations were made with three gravity meters in a double loop including two other stations in the area. The standard error for the stations NBS-1 and NBS-2 was 0.03 mGal and that for the sub-subbasement of the East Building was 0.02 mGal.

The optical axis of the absolute gravity apparatus was 12.1 cm above the support plate which, in turn, was 220.4 cm above the floor. The machine, therefore, measured gravity at a point 232.5+ 14.2 cm above the floor. An adjustment of +0.0007 cm/s2 based on the observed gravity gradient of 0.28 mGal/m of elevation was applied to the absolute result to correct it to station NBS-2. The absolute value of gravity for station NBS-2, as determined by the experiment, and the coordinates of NBS-2 are:

9. Conclusion

A measurement of the absolute value of the acceleration due to gravity has been made and referenced to a permanent gravity meter station on the grounds of the National Bureau of Standards near Gaithersburg, Maryland. The value established for the reference station is 980.1018 cm/s2 with a standard deviation of 0.0005 cm/s2. This result, transferred to the top of the east elevated pier in the gravity room of the Department of Commerce Building, Washington, D.C., gives a value of 980.1048 cm/s2 with the same standard deviation.

The author is deeply indebted for the helpful advice and assistance given by the staff of the National Bureau of Standards during the course of the work. He is particularly indebted to Mr. J. H. Troxell, who made the length measurements during the final determination.

10. References

[1] P. G. Roll, R. Krotkov, and R. H. Dicke, The equivalence of inertial and passive gravitational mass, Ann. Phys., 26, 442-517 (1964).

[2] A. H. Cook, The absolute determination of the acceleration due to gravity, Metrologia, 1, 84-114 (1965).

[3] F. Kühnen and P. Furtwängler, Bestimmung der absoluten Grösze der Schwerkraft zu Potsdam (Veröffentlichung des

K. Preuszischen geodätischen Institutes, N. F. no. 27)
Berlin: P. Stankiewicz, 1906.

[4] P. R. Heyl and G. S. Cook, The value of gravity at Washington, J. Res. NBS 17, 805-39 (1936)RP946.

[5] J. S. Clark, An absolute determination of the acceleration due to gravity, Phil. Trans. Roy. Soc. London, Ser. A., 238, 65-123 (1939).

[6] H. L. Dryden, A reexamination of the Potsdam absolute determination of gravity, J. Res. NBS, 29, 303–14 (1942)RP1502. [7] H. Jeffreys, On the absolute measurement of gravity, Monthly Notices Roy. Astron. Soc., Geophysical Suppls., 5, 398–408 (1949).

[8] P. N. Agaletskii and K. N. Egorov, Rezultaty absoliutnykh opredelenii uskoreniia sily tiazhesti v punkte VNIIM (Leningrad), Izmeritel Tekhn., Vol. for 1956, no. 6. 29-34.

[9] A. I. Martsiniak, "Opredelenie absoliutnoi velichiny uskorenia sily tiazhesti po padeniiu zhezla v vakuume," Izmeritel Tekhn. Vol. for 1956, no. 5, 11-15.

[10] H. Preston-Thomas and others, An absolute measurement of the acceleration due to gravity at Ottawa, Can. J. Phys. 38, 824-52 (1960).

[11] Å. Thulin, Une détermination absolue de g au pavillon de Breteuil, par la méthode de la chute d'une règle divisée, Ann. Geophys. 16, 105-27 (1960).

[12] J. E. Faller, An Absolute Interferometric Determination of the Acceleration of Gravity. Thesis, Princeton University, 1963.

[13] A. H. Cook, A new absolute determination of the acceleration due to gravity at the National Physical Laboratory, England, Phil. Trans. Roy. Soc. London, Ser. A., 261, 211–252 (1967). [14] C. Volet, L'intensité de la pesanteur déterminée par l'obser vation de la chute d'un corps, Comptes rendus de l'Académie des sciences, 224, 1815-16 (1947).

[15] A. Sakuma, Etat actuel de la nouvelle détermination absolue de la pesanteur au Bureau international des poids et mesures. International Association of Geodesy, Bulletin géodésique, n.s., no. 69, 249-60 (1. sept. 1963).

[16] A. H. Cook, Recent developments in the absolute measurement of gravity, International Association of Geodesy, Bulletin géodésique, n.s. no. 44, 34-59 (1. juin 1957).

(Paper 72C1-264)