On the effect of the internal friction of fluids on the motion of pendulums / by G.G. Stokes.

  • Stokes, George Gabriel, 1819-1903.
Date:
1851
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Licence: Public Domain Mark

Credit: On the effect of the internal friction of fluids on the motion of pendulums / by G.G. Stokes. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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    1 I 62 PROFESSOR STOKES, ON THE EFFECT OF THE INTERNAL FRICTION Baily’s results with spheres suspended by fine wires. i Diameter of sphere. 2a n By theory. No. and kind. Diameter of wire. 2ai For buoy- ancy. For inertia on common theory. Additional for inertia on account of internal friction. Correc- tion for wire. Correction for confi- ned space (esti- mated.) Total. n By expe- riment. Difference. ]L-inch spheres. No. 1, Platina. 1-44 0-01429 1 0-5 0-289 0-035 0-011 1-835 1-881 + 0-046, or -1- ^ No. 2, Lead. 1-46 0-01429 1 0-5 0-285 0-035 0-011 1*831 1-871 + 0-040, or -1- ^ + 0-004, or + -f 0 060, or + No. 3, Brass. 1*465 0-01429 1 0-5 0-284 0-035 0-011 1-830 1-834 No. 4, Ivory. 1*46 0-00251 1 0*5 0*285 0-016 0-011 1-812 1-872 2-inch spheres. No. 5, Lead. 2-06 0*01429 1 0-5 0-202 0-012 0 032 1-746 1-738 - 0-008, or - 2^ No. 6, Brass. 2-065 0*01429 1 0-5 0-202 0-012 0-032 '1-746 1-751 + 0-005, or -h No. 7, Ivory. 2-06 0-01429 1 0*5 0-202 0-012 0-032 1-746 1-755 + 0-009, or -f- 3-inch sphere. No. 66, Brass. 3*030 0-023 1 0-5 0-137 0-005 0*101 1-743 1-748 + 0-005, or -t- ■' The mean error in different determinations of R for the same sphere was about O’Ol or 0 02, and this does not include errors arising from small errors in specific gravities, &c. Hence, if we except the spheres Nos. 1, 2, and 4, the discrepancies between theory and experiment are altogether insignificant. In considering the confirmation thence arising to the theory, it must be borne in mind that the theory did not furnish a single disposable constant, inasmuch as .y/ju' was already determined from the experiments with cylindrical rods. The result obtained with the brass sphere No. 3 happens to agree almost exactly with theory. However, as the results obtained with this sphere exhibited some anomalies, it seems best to exclude it from consideration. The value of It, then, which belongs to a iLinch sphere, appears to exceed by a minute quantity the value deduced from theory. The difference is indeed so small that it might well be attributed to errors of observation, were it not that all the spheres tell the same tale. Thus the error + 0-046 in the case of the platina sphere corresponds to an error of less than the fortieth part of a second in the observation of an interval of time amounting to 4i hours. If the apparent defect, amounting to about 0'04 or 0‘05, in the theoretical result be real, it may be attributed with probability to an error in the correction for the wire. This would be no objection to the theory, for it will be remembered that the theory itself indicated the probable failure of the formulae generally applicable to a long cylinder when the cylinder comes to be of such extreme fineness as the wires employed in pendulum experiments. 58. The preceding experiments of Baily’s are the most important for the purposes of the present paper, inasmuch as they were performed on pendulums of simple and very different forms; but there still remain three sets of experiments, the fourteenth, fifteenth, and six- teenth, in which the pendulum consisted of a combination of a sphere and a rod, so that the results can be compared with theory. The details of these experiments being suppressed, I L