IX.On the steady rotation of an anchor ring in a viscous liquid

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Abstract
The anchor ring rotates slowly about its axis, and the path of each particle of the liquid is taken as a circle parallel to the equatorial plane. The solution depends upon Laplace's equation for a uniplanar vector, and the analysis is developed partly in cylindrical coordinates and partly in ring coordinates. An expression for a multiple of the velocity is obtained as a cosine series in which the coefficients are Beta and Riemann P-functions. Two solutions are employed, valid in different regions; the one applies to an annulus with a viscous liquid core, the other to a liquid at rest at infinity. The validity of the result is limited by the ignoration of the inertia terms.

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