The inverse-square law of gravitation is tested at submillimeter distances. To minimize Newtonian errors, the experiment employs a near null source, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a nominal distance of 180 micrometers. The source mass amplitude of motion is 16.1 micrometers. The signal is detected by a superconducting differential accelerometer. Careful matching and alignment makes the detector highly immune to platform vibrations. To reduce the thermal Brownian motion noise as well as the temperature noise of the instrument, the experiment is cooled to 1.7 K by pumping on liquid helium.

In this dissertation, I discuss the assembly, design, and design improvements of the inverse square law experiment. I perform a comprehensive analysis of the errors, identify the problems with the apparatus, and show ways to improve the design of the experiment. With the improved design, it will be possible to achieve a sensitivity of |alpha| = 2 x 10^-3 at lambda = 150 micrometers, which will improve the current experimental limits by one order of magnitude at 150 micrometers and by over two orders of magnitude at shorter distances.