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The inverse-square distance dependence of the gravitational force has been tested over a range of approximately 2 to 5 cm, by use of a test mass suspended from a torsion balance to probe the gravitational field inside a mass tube. The result supports an inversesquare law. Assuming a force deviating from inverse square by a factor ll + e lnr(cm)] it is found that e = (1± 7)x 10' 5 .PACS numbers: 04.90.+e, 06.30.-k A number of different ideas have recently been discussed which suggest the existence of forces which could manifest themselves as a deviation from inverse-square distance dependence of the gravitational force on a laboratory distance scale (1 cm-1 km). These ideas include modified theories of gravity 1 ; exchange of a low-mass axion, of a variety undetectable in other tests 2 ; and a long-range component of the strong interaction, arising from two-gluon exchange. 3 Of particular interest is the observation by Scherk 4 that supergravity unification theories lead naturally to an effective weakening of the gravitational force at short distances, possibly on a laboratory scale, so that inverse-square tests might provide evidence for such theories.An experiment indicating a breakdown of the inverse-square law has, in fact, been reported by Long. 5 Comparing the effective gravitational constant at two distances, Long finds G(4.5 cm) to be smaller than G(30 cm) by (0.37±0.07)%. This result has inspired a number of other inverse-square tests, 6 but to our knowledge no result with sensitivity comparable to Long's has been reported. We report here an experiment defining a range of distances (close to Long's) and a condition (null experiment) in which, with sensitivity greater than Long's, we find no anomaly.Our experiment uses a torsion balance (Fig. 1) to measure the change in the force acting on a test mass suspended inside a long hollow cylinder, as the cylinder is moved laterally. For an infinitely long perfect cylinder and exact inversesquare force law, the gravitational field due to the cylinder vanishes everywhere inside it, just as inside a spherical mass shell. For our finite cylinder of length L = 60 cm and inside diameter D = 6 cm there exists a small net "end-effect" force on a test mass located near an inside wall, smaller than the nearly balanced opposing forces due to near and far walls by a factor (D/L) 2 = 10" 2 . Thus to compare the gravitational force at the distances from the near and far walls in our cylinder, to a level of 1 part/10 5 , we need measure the end effect force to only 1 part/10 3 . Furthermore, the residual field in the cylinder is such that we need measure only the relative motion of the cylinder to just 1 part/10 3 , while the absolute position of the cylinder relative to the test mass need only be known to a few millimeters. (The homogeneity and geometry of the cylinder itself must be known with precision on the order of 1 part/10 5 .) By averaging data taken at a set of equally spaced azimuthal orientations of the cyl-

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A major effort is underway to develop highly portable absolute gravimeters having an ultimate accuracy of 3–5 μGal, an accuracy which translates into a height sensitivity of several centimeters. We are just finishing the construction of six such units. Measurements at the Joint Institute for Laboratory Astrophysics with one of these new instruments agree well with the earlier measurements made in 1981 and 1982 with a previous generation instrument. Recent measurements at the International Bureau of Weights and Measures in Sevres, France, as a part of an international intercomparison of absolute gravimeters, also show good agreement with the other instruments.

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