= W. M. Macek
{c}
<W. M. Macek> coauthored <Rotation Rate Sensing with Traveling-wave Ring Lasers by W. M. Macek and D. T. M. Davis, Jr.> with <D. T. M. Davis, Jr.> in 1963. Their Sperry Gyroscope Company experiment used the $1.153\,\mathrm{\mu m}$ line of a <helium-neon laser> in a metre-square <optical cavity>. Four gas tubes and four corner mirrors maintained the ring path, and the outputs were combined for detection.<Rotation Rate Sensing with Traveling-wave Ring Lasers by W. M. Macek and D. T. M. Davis, Jr.>[Printed p. 67, original byline, apparatus paragraph and Figure 1]{ref}
Their contribution illustrates the distinction between a passive <Sagnac interferometer> and an active <ring laser gyroscope>: the circulating optical fields are sustained by laser gain, and their frequency splitting provides a rotation signal. In the ideal planar model, the magnitude of the split is
$$
|\Delta f|=\frac{4A|\Omega_n|}{\lambda P},
$$
where $A$ is the enclosed area, $P$ the ring perimeter, $\lambda$ the <wavelength> and $\Omega_n$ the component of <angular velocity> normal to the ring. This follows by converting the <Sagnac effect>'s counterpropagating travel-time difference into a resonant frequency difference.
For an original ideal scale calculation using the reported square size and <wavelength>, take $A=1\,\mathrm{m^2}$, $P=4\,\mathrm m$ and $|\Omega_n|=10^{-4}\,\mathrm{rad/s}$. Then $|\Delta f|\approx86.73\,\mathrm{Hz}$. Doubling the side of a square doubles $A/P$ and this scale factor. These are model calculations, not reported sensitivity or accuracy figures. The joint paper establishes the demonstrated apparatus, without assigning its component tasks to either author separately.
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