. Contributions. ti,.. .n,,:;,,n mi ?l,i ,.,^\\v ^^ Fig. curves for steel. have been magnified, but what was gained in this way was lost in (inini-tion of the trace. The largest double amplitude measured was about4 mm. on the film, the smallest about mm. Ordinarily the measure-ments ran from 3 mm. to mm. The measuring engine read dircxtly to mm. Two records were made for each mass suspended from the copper wire,because the rapid damping allowed room for two on the Mm. For theother metals the damping was so small that only one record was madeon each film. E
. Contributions. ti,.. .n,,:;,,n mi ?l,i ,.,^\\v ^^ Fig. curves for steel. have been magnified, but what was gained in this way was lost in (inini-tion of the trace. The largest double amplitude measured was about4 mm. on the film, the smallest about mm. Ordinarily the measure-ments ran from 3 mm. to mm. The measuring engine read dircxtly to mm. Two records were made for each mass suspended from the copper wire,because the rapid damping allowed room for two on the Mm. For theother metals the damping was so small that only one record was madeon each film. Every 30th vibration was measured and the logarithms ofthese were averaged by pairs, so that the plots show only the logarithmsfor every 6oth vibration. Figs. 14 and 15 represent graphically thedecrements for the masses given in Table XI. in order of increasingmagnitude. Similar curves were drawn for copper, and the logarithmicdecrements of Table XI. were obtained from these curves. 430 GEORGE A. LINDSAY. [|^^ W. Fig. 15. Decrement curves, O, for platinum-iridium; A, for phosphor bronze. The scale is thesame for all; but to avoid confusion the origin of ordinates has been shifted up or down forcertain curves, as indicated by the logarithms in brackets. Variation of the Logarithmic was found by Schmidt^ for torsional, and later also b} \^oight^ forflexural and torsional vibrations, that the logarithmic decrement variedwith the amplitude. They expressed the relation in the form X = Xo + hA\ where Xo is the logarithmic decrement for ver\ small vibrations. The values of Table XL for copper are plotted in Fig. i6. Althoughthe rate of increase is different for different masses, the increase is nearlyproportional to the increase in amplitude in all cases, and X = Xo + ^^ represents the relation. The second mass gave an abnormally largedecrement for the larger amplitudes, as seen from Table XI. There isno apparent reason for this. Both records taken of this mass show thesam
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