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On the Period of a Rod Vibrating in a Liquid

Mary I. Northway, A. Stanley Mackenzie

1901
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Physical Review
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AS early as 1786 Buat announced in his " Principes d'Hydraulique " that the period of a pendulum was greater when vibrating in a fluid than when vibrating in a vacuum, not only because of the loss in weight due to buoyancy but also because of the mass of fluid which must be considered as participating in the motion of the pendulum. The latter is loaded by, or drags with it" a certain amount of the fluid. Buat determined this added mass for the case of a sphere and for bodies of other forms.
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... of other forms. Little attention was paid to this work until Bessel 1 about forty years later, in determining the length of the seconds pendulum, concluded from theoretical reasons that it was necessary to take into account the inertia of the air as well as its weight. When the dimensions of the bob were small in comparison with the length of the suspending wire, Bessel represented the apparent increase in the weight of the pendulum by a constant, k, times the mass of the displaced fluid. For a sphere 2 in. in diameter vibrating in water he found for k the: value 0.9459 ; later he changed this to 0.956. Sabine 2 tried to find the effect of air on a pendulum by making it; vibrate in air and then in a vacuum. He found that the old correction for buoyancy should be multiplied by a factor m y whose value was 1.655, in order to obtain the total correction. In 1832 Baily 3 published the results of some similar experiments. Four spheres of about 1.5 in. in diameter gave for m the value 1.84 ; and three spheres of about 2 in. in diameter gave 1.748. For spheres of about the same size Bessel had found the value 1.956. For small cylinders Baily found the value of m to increase regularly with decrease of diameter, but according to no apparent law. iAbh. d. Akad. d. Wiss., Berlin, 1826; Coll. de Mem. Soc. Fr. de Phys., 5, 1. 2 Phil. Trans., 1829 ; Coll. de Mem. Soc. Fr. de Phys., 5, 134. 3 -Phil. Trans., 1832, p. 399; Coll. de Mem. Soc. Fr. de Phys., 5, 185.

doi:10.1103/physrevseriesi.13.145
fatcat:dkjpfjqgrnc65kvm7xfjz2biu4