has frequently been questioned, experiments such as those with the Eötvös pendulum [1]' indicate that any effects must be less than one part in 1011. This amount is several orders of magnitude less than the sensitivity of any absolute measurement now under consideration.

1.2. Previous Determinations

The history of absolute gravity experiments published within the past 70 years has been reviewed by several authorities. Cook [2], in particular, gives a very thorough treatment. Briefly summarized, an absolute determination published in Potsdam, Germany, in 1906 by Kühnen and Furtwängler [3] became the base for the world network of relative gravity observations. Two later determinations, one by Heyl and Cook [4] at Washington, D.C. and the other by Clark [5] at Teddington, England, disagreed with the Potsdam result by significant amounts. Reexamination of the Potsdam result by Dryden [6] and of Clark's and Heyl's results by Jeffreys [7] improved the agreement but did not fully resolve the questions raised.

In 1956 the results of three new determinations by Agaletskii and Egorov [8] and Martsiniak [9] tended to support the conclusion that the original Potsdam result is too high by some ten to twenty parts per million. Three other absolute determinations appeared within the next few years, Preston-Thomas et al. [10], Thulin [11], and Faller [12]; all have shown reasonably good agreement with each other and have ranged from about 12.7 to 14.5 milligals 2 (mGal) below the Potsdam result. More recently Cook [13] has reported the result of a determination at the National Physical Laboratory differing from the Potsdam result by approximately 13.7 mGal.

1.3. Accuracy and Precision

The requirements for accuracy in absolute gravity measurements are much the same for the geodesist and the metrologist. An accuracy of one part in a million is critically needed and an accuracy of one or two parts in ten million would be most desirable. It has been suggested that some form of absolute gravity apparatus which can readily be transported and set up in different sites might resolve the apparent bias between some measurements with geodetic pendulums. If such an approach is to be effective, a demonstrated stability in the portable absolute apparatus of one part in ten million is quite essential.

The results of absolute determinations in which measurements of several non-related parameters are combined to obtain an estimate of the magnitude of a presumed constant quantity, the true value of which is unknown, cannot realistically be assigned a level of accuracy. One can and does derive an index, such as the standard deviation, of the precision of individual determinations made over a short period of time. From this index an estimate may be derived of the precision which might be expected for the means of similar sized

Figures in brackets indicate the literature references at the end of this paper. * A milligal is a geodetic unit of gravity equal to 10 cm/s2, approximately 1 ppm of the value of g.

groups of measurements drawn from the same sour If such groups of measurements are actually ma separated by periods of a day or more, the stand deviations of the individual measurements may much the same but the means of the groups will of show more scatter than would have been predic from the internal consistency of any of the gro The conclusion is that the composition of the pop tion from which the samples have been drawn changed with time. It is inferred that there m exist sources of bias which vary from day to day which do not change appreciably over the cours a single set of measurements.

The nature and extent of variability of this usually remain unknown. The demonstrated pres analyse it by looking for correlation with other pa of bias, of course, arouses the investigator to tr eters. In general, though, this process has alr been carried out to the limits of practicality. residuum of bias is probably a major cause of the known tendency of the scientist to continue measurements indefinitely.

In a broad sense, therefore, one can consider an estimate of the accuracy of an experimental n urement can be made only when the resultant can be compared to a defined or assumed true In the absence of such a true norm, a determin obtained from a series of measurements made w single piece of apparatus must be regarded as o sample from an unknown population. Estimat the precision should be made, together with stater of the sensitivity to variations in the comp measurements in relation to the precision with those standards were established. Such stater give limits to the error only from known sources final appraisal of the limits of knowledge abo true value of the constant determined must come the results of a group of completely indepe experiments differing in method, location, and personnel conducting them.

1.4. Methods for Gravity Determinations

Taken without regard for experimental diffic would appear that the most direct method for mining the absolute value of the acceleration gravity would be to observe the motion of some moving without constraint under the action gravitational field of the earth. Up to about 19 use of such a method was impracticable becaus difficulty in measuring the short lengths of ti volved. Virtually all gravity measurements were with some form of pendulum.

Basically the pendulum method substitutes a with a maximum of constraint for a system minimum of constraint. From a purely practica point the pendulum method offers many adva An uncertainty of one part in a million in the m ment of the pendulum length produces the relative uncertainty in the determination of uncertainty of one part in a million in the measu of time results in an uncertainty of two parts in lion in g, but the length of the time interval

increased to the point where timing errors become negligible. The difficulties of the pendulum method lie in the complex theoretical corrections for pendulum flexure and the uncertainties contributed by motion of the pendulum support and by the indefinite point of rotation at the knife edge.

Experiments involving unconstrained motion under gravitational forces have, with the perfection of frequency counting electronic circuitry, developed in many diverse forms. The most elementary form of such an experiment would be one in which an object is released from rest and allowed to fall a known distance in a vacuum. If time is measured from the instant of release to the point where the object has travelled the measured distance, the acceleration may be computed from the simple relationship

2d 12

Here the sensitivity in the determination of g is the same as in the case of the pendulum and the efficiency of measurement would be high. Unfortunately the experimental difficulties in the measurement of time and length and in the release of the object are so formidable that no investigator up to the present has undertaken such an experiment.

The restrictions of the elementary free-motion experiment can be eliminated by releasing the object prior to the start of the time measurement. In this case the object acquires an initial velocity of unknown magnitude which can be successfully eliminated by the addition of one or more distances over which time is measured. A parallel and equally effective approach is to measure the distance the object travels during two or more known intervals of time.

These techniques, while successfully eliminating the experimental difficulties of the elementary experiment, are introduced at the cost of an increase in sensitivity to errors in the measurement of length and time. The method offers many advantages from the experimental viewpoint and has been employed in one form or another by several investigators.

In 1947 [14], M. Charles Volet, then Director of the Bureau International des Poids et Mesures, suggested that if an object were projected upwards, passing two position sensing stations separated by a known distance and then allowed to fall back, and the time between successive passages at each level recorded, a considerable increase in measurement efficiency would be obtained. The method is indeed a most effective one since the sensitivity to length errors is the same as for the elementary experiment and the sensitivity to timing errors is very nearly equal to that in an elementary experiment with four times the height of fall. The principal disadvantage is the increased difficulty in the experimental technique required. The method is currently being employed in experiments at the National Physical Laboratory by Cook [2], and at the Bureau International des Poids et Mesures by Sakuma [15]. Sakuma's method embodies the concept of making the moving object one reflector of an

interferometer system illuminated by a gas laser light source. This approach has the great advantage of making the length and time measurements occur simultaneously and avoids the limitations of an intermediate length standard. Faller's experiment [12] was the first published determination using the falling interferometer plate principle. He was limited to a very short length of drop by the necessity of using a conventional light source.

2. The NBS Determination

2.1. General Description

Following a review and appraisal of several possible approaches to absolute gravity measurements, it was decided to employ a modification of the direct free-fall method with the release of the object preceding the timing sequence. The method makes use of a concept introduced by Agaletskii and Egorov [8] in which the released object falls within a chamber which is itself falling. Agaletskii's technique was to determine the acceleration of the object with respect to the chamber and, separately, to determine the acceleration of the chamber with respect to the earth. The measurements were made by a multiple flash method at constant frequency.

In the experiment at the National Bureau of Standards the acceleration of the inner falling object was determined directly with respect to the earth from measurements of the time required for two intervals of length on a fused silica tube to pass an optical sensing station.

The apparatus for the experiment was first set up at the National Bureau of Standards in Washington, D.C., in 1961 in a pair of small rooms known as the sub-subbasement of the East Building. This had been the site of the absolute determination by Heyl and Cook [4]. In February of 1964 the apparatus was damaged in a flood which left the site in a nearly unusable condition. The apparatus was reconstructed in the summer of the same year and installed in room 129 of the Engineering Mechanics Building (Building 202) at the new site of the Bureau near Gaithersburg, Maryland. The measurements leading to the final value were taken during April, May, and June of 1965.

In the experiment a fused silica tube slightly more than a meter in length rested on a seat in a vacuum chamber a few centimeters longer than the tube. The vacuum chamber was mounted on a carriage and held by a latch at the top of a pair of vertical guide rods secured in a rigid frame. The arrangement was such that when the latch was released, the carriage was free to descend vertically down the guide rods under the influence of gravity. A schematic diagram of the apparatus is shown in figure 1. Friction between carriage and guide rods was reduced to a low level by antifriction bearings. In the latched position the carriage was under an additional downward force provided by an adjustable, short-travel, spring-loaded plunger. When the latch was released the carriage moved downward with an acceleration about ten per

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FIGURE 1. Schematic view of gravity apparatus.

cent greater than the acceleration due to gravity for the first 8 mm of its travel. The additional acceleration of the car effectively separated the fused silica tube from its seat inside the chamber, leaving the tube floating without contact with the chamber for the duration of the fall of the carriage. By proper adjustment of the spring plunger travel, the relative displacement between the silica tube and the chamber. could be restricted to a millimeter or so after the initial separation. After a fall of about 14 m the carriage was brought to a smooth stop by an air dash-pot.

Only the force due to gravity acted upon the silica tube inside the chamber. The tube, which was opaque, carried three transparent slits, to be described later. The slits defined two lengths, one extending from the slit near the lower terminus of the tube to the second slit 30 cm above it, and the other extending from the lower slit to the third slit 100 cm above it. The vacuum chamber was provided with pairs of ports at locations opposite the slits. A single position-sensing station consisted of a light source, a long focus microscope, and a photomultiplier cell. As each slit passed the station, an illuminated image of it was projected on a plane containing a stationary slit within the microscope tube. Beyond this reference slit was the photomultiplier cell. The reference slit was dark until the bright image of a moving slit swept across it, causing the photomultiplier cell output to rise from nearly zero to full anode potential. A two-channel electronic

timer system was triggered at some predetermine potential level near the midpoint of the linearly risin photocell output curve.

During the fall of the tube, both timer channe were started by the passage of the lower slit past th position-sensing station. One channel was stopped the passage of the second slit and the other chann was stopped by the passage of the third slit. Th thus registered the transit time for the 30-cm a 100-cm lengths, respectively.

The apparatus was arranged so that the fused sili tube fell a distance of 6.8 cm before the first s initiated the timing sequence. Thus about 118 elapsed between the release of the latch and the st of the time measurements.

The lengths corresponding to the two distances the fused silica tubes were measured, using the sa apparatus employed for the free fall time measu ments. The fused silica rod was secured firmly in seat and a measurement made of the distance carriage moved between the locations where timers would have been triggered by the photo signals. The technique for the length measureme is described in another part of this paper. The met has the advantage of including effects of the vacu on the actual length of the rod as well as any opt effects from the ports in the vacuum chamber w More importantly, it is a direct measurement of quantity desired.

The following summary indicates the magnitu of the parameters measured and the sensitivity the result in terms of the least count in the m urements.

clear, fused silica tubing having an outside diameter of 15 mm, and a wall thickness of 1 mm. Each tube had a length of 107 cm. A metal sleeve with an outside diameter of 19 mm fitted over one end of each tube and was cemented in place with epoxy cement. The external end of the sleeve was machined to a spherical radius of 12 mm. The sleeve formed the lower support tip for the silica tube.

At a point about 11 cm from the other end of the silica tube a second sleeve was attached, fitted with guide pins for alinement and rotation in the vacuum chamber. Figure 2 shows a schematic view of an assembled tube.

Each silica tube was fitted with three rectangular clear apertures formed by pairs of bevel-edge metal plates cemented to the outer surface of the tube wall. The plate edges were perpendicular to the longitudinal axis of the tube and spaced so that the aperture took the form of a transverse slit about 1 mm wide and 7 mm long. In the experiment the dimensions of the slit were of no particular consequence, as the timing sequences were generated by the transition from dark to light as the lower edges of the slits passed the optical axis of the position sensing optical system. The upper slit boundary was supplied to provide a sharp cut-off of the light beam in order to prevent spurious triggering of the timers by photo-tube noise in a slowly decaying light pattern.

1

I METER

30cm

FIGURE 2. Free-fall object showing slits and guide sleeves.

The experiment required that the critical edges of all three slits be mutually parallel, coplanar, and perpendicular to the axis of the fused silica tube. To this end, a special jig was made to hold the silica tube and aperture edges during the operation of cementing the edges to the tube.

The jig consisted of a channel-shaped frame of steel having two vee-blocks attached on the centerline of the channel web at positions corresponding to the lower support tip and the upper guide sleeve of the silica tube. Three pairs of rectangular notches were machined into the flange-edges of the channel at locations corresponding to the 0-, 30-cm, and 1-m aperture locations on the silica tube. The parallelism of the jig notches was checked with an autocollimator and the notches hand-finished to be parallel within 7 s of arc. This amount corresponds to an error of 0.03 μm in 1 mm.

In using the jig, cut and finished aperture edges were attached to special holders. These were flat bars which could be set into the jig notches and secured in place with hold-down screws to maintain alinement during the setting of the cement. The holders were constructed with flats lapped on the leading edges at the points where they contacted the forward edges of the jig notches. The center portion of the holder edges was relieved. An aperture edge was attached to each of three such holders by metal fingers which gripped the aperture plates at the sides, the defining edges of the aperture plates being made coplanar with the lapped flats on the holders by a light lapping operation. The finished assemblies were then checked in a comparator.

A silica tube, complete with supporting tip and guide sleeve, was clamped in the vee-blocks which had been shimmed to provide a clearance of about 0.07 mm between the surface of the silica tube and the under face of the aperture plate and holder assemblies. A dot of epoxy cement was then placed on the center of each aperture plate mounted in its holder. The three holders were inverted and each carefully placed in a jig notch and secured in place with the lapped edges forced against the leading edge of each notch.

After the cement had set for 24 hr, the gripping fingers coupling the holders to the aperture edges were released and the holders removed from the jig. The bond between the silica rod and the aperture plates was then reinforced with additional cement. Three opposing aperture plates to complete the framing of the apertures were then installed by a similar technique. The bond formed between the metal aperture edge plates and the silica tube by the epoxy cement was quite strong. Even the bond formed by the initial small dot of cement had sufficient strength after 3 or 4 days to require considerable force to separate the two parts.

As a final step each silica tube was given several coats of silver conductive paint to prevent the formation of localized electrostatic charges. Preliminary experiments with silica rods or tubes in vacuum had shown that under certain conditions a substantial electrostatic charge was generated by the separation

of the supporting tip of the tube from the seat in the vacuum chamber. Even though the falling object was surrounded by the grounded metal vacuum chamber, the internal field was not necessarily zero and the silica tube tended to be drawn out of the true vertical line as it fell. In some cases the effect was so severe as to cause the timers to malfunction. The conductive paint, which reduced the surface resistance of the silica tube of less than 10 N, eliminated this difficulty. Only the clear apertures and corresponding areas on the opposite face of the tube were not coated.

2.3. The Vacuum Chamber

The vacuum chamber was fabricated in three sections joined by flanges with O-ring seals. It was constructed of brass tubing having an outside diameter of 4.76 cm and a wall thickness of 0.32 cm. The outside of the chamber was covered by two layers of 3-mm cork sheet and finally by a layer of heavy aluminum foil to reduce the effects of ambient temperature fluctuations. The vacuum chamber assembled on the carriage of the machine is shown in figure 3.

The lower section of the chamber contained the support cone for the silica tube, the vacuum gage, the vacuum pump connection, and the optical windows for the zero and 30 cm apertures of the silica tube. The middle section of the vacuum chamber housed the upper guide bearing for positioning the silica

FIGURE 3. Upper portion of gravity machine showing guide rods, carriage, and vacuum chamber.

tube preparatory to release. In the upper section the vacuum chamber were the optical windows f the 1-m aperture of the silica tube.

The vacuum chamber was so arranged that it w necessary to disassemble only the upper section order to remove or insert a silica tube.

The support cone formed an integral part of t removable base closure for the lower section of t vacuum chamber. It was made by machining a b with a recess in the form of a 90° vertex angle co The major portion of the cup formed in this way then milled out, leaving only three ribs, 120° ap and about 7 mm wide. The shape was a comprom between the desirable 3-point support and a cone seat. It was considered that a 3-point supp would tend to produce localized deformations of silica tube support tip which would in time make contact unstable. Earlier experiments with a sup seat which more nearly approximated a full cone likewise resulted in some undesirable characterist

The upper guide bearing mechanism was as a unit into the middle section of the vacuum ch ber. It consisted of two end flange plates with O seals each connected by a metal bellows to a ce sliding unit. A section of brass tubing of the dimensions as the other sections of the vac chamber was attached between the end flange p providing structural support and also guidanc the central sliding unit. The central sliding terminated in a tube having an inside diamet 19 mm which projected above the end flange into the upper portion of the vacuum chambe this tube was attached a bushing having an diameter just slightly larger than the upper of the silica tube. The upper surface of the bu was a double-vee cam surface to engage the pins of the silica tube sleeve as shown in fig

When a silica tube is installed in the asse vacuum chamber, the arrangement is such that the central sliding unit is moved to the upper li its travel, the silica tube is picked up by the pins in the vee-shaped notches and rotated in proper orientation with respect to the optical the position sensing station. Then, as the sliding unit is lowered, the silica tube is seated support cone at the bottom of the vacuum cham is precisely alined by the guide bushing surro the sleeve on the silica tube. When the central unit reaches the lower limit of travel where it locked in place, the guide bushing is com disengaged from the silica tube sleeve and th tube stands supported only by the support c is then ready for a free-fall measurement.

During length measurements on the silica t central sliding unit was left in the center of it where the silica tube received lateral guidan the bushing but rested on the support cone.

The six optical windows in the vacuum c were Pyrex glass discs, 4.5 mm thick and 19 diameter. They were optically polished to within one-half wave length of the green mercu The discs were inserted in machined wells in th