In this paper formulae are obtained for the velocity-potential at the surface of a free-edge disc vibrating with nodal lines in a fluid. These formulae are used to ascertain the accession to inertia due to the fluid when the disc is set in an infinite rigid plane. The equivalent mass and the mass coefficient of the disc vibrating in vacuo are found also. By means of these results, the influence of the fluid on the frequency of vibration with ( a ) one nodal circle, ( b ) one nodal diameter, ( c ) stationary centre, is evaluated. In air the alteration in frequency is almost negligible, whereas in water the frequency is reduced to a small fraction of its value in vacuo .
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N. W. McLachlan (1932) studied this question.