A gyroscope is mounted in a sphere, lined with Mu-metal to reduce magnetic influence, connected by a spindle to the vertical axis of the theodolite. The battery-powered gyro wheel is rotated at 20,000 rpm or more, until it acts as a north-seeking gyroscope. A separate optical system within the attachment permits the operator to rotate the theodolite and thereby bring a zero mark on the attachment into coincidence with the gyroscope spin axis. By tracking the spin axis as it oscillates about the meridian, a record of the azimuth of a series of the extreme stationary points of that oscillation may be determined by reading the theodolite azimuth circle. A midpoint can later be computed from these records that represents a refined estimate of the meridian. Careful setup and repeated observations can give an estimate that is within about 10 arc seconds of the true meridian. This estimate of the meridian contains errors due to the zero torque of the suspension not being aligned precisely with the true meridian and to measurement errors of the slightly damped extremes of oscillation. These errors can be moderated by refining the initial estimate of the meridian to within a few arc minutes and correctly aligning the zero torque of the suspension.